PES Skill Sheets.book - Capital High School

Chapter and Section 

Chapter 1: Measurement 

1.1 Measurement • Lab Safety • Using Your 

Textbook 

1.2 Time and Distance • Measuring Length • Averaging • SQ3R Reading and 

Study Method 

1.3 Converting Units • Dimensional 

Analysis 

• Fractions Review 

• Significant Digits 

1.4 Graphing • Creating 

Scatterplots 

• What’s the Scale? 

Chapter 2: The Scientific Process 

2.1 Inquiry and the Scientific 

Method 

2.2 Experiments and 

Variables 

2.3 The Nature of Science 

and Technology 

• Recording 

Observations in the 

Lab 

• Lab Report Format 

• Using a 

Spreadsheet 

Physical, Earth, and Space Science Skill and Practice Worksheets 

• Study Notes 

• Science Vocabulary 

• SI Units 

• Scientific Notation 

• Stopwatch Math 

• Understanding 

Light Years 

• SI Unit Conversion 

Extra Practice 

• SI-English 

Conversions 

• Interpreting Graphs 

• Recognizing 

Patterns on Graphs 

• Scientific 

Processes 

• What’s Your 

Hypothesis? 

• Identifying Control 

and Experimental 

Variables 

• Indirect 

Measurement 

i


Chapter 3: Mapping 

3.1 Maps • Position on the 

Coordinate Plane 

ii 


• Latitude and 

Longitude 

• Map Scales 

• Vectors on a Map 

3.2 Topographic Maps • Topographic Maps 

3.3 Bathymetric Maps • Bathymetric Maps • Tanya Atwater 

Chapter 4: Motion 

4.1 Speed and Velocity • Solving Equations 

With One Variable 

• Problem Solving 

Boxes 

• Problem Solving 

with Rates 

• Percent Error 

4.2 Graphs of Motion • Calculating Slope 

From a Graph 

• Speed 

• Velocity 

• Analyzing Graphs 

of Motion With 

Numbers 

• Analyzing Graphs 

of Motion Without 

Numbers 

4.3 Acceleration • Acceleration 

• Acceleration and 

Speed-Time 

Graphs 

• Navigation 

• Acceleration Due to 

Gravity


Chapter 5: Force 

5.1 Forces • Ratios and 

Proportions 


• Internet Research 

• Bibliographies 

5.2 Friction • Friction 

• Mass vs. Weight 

• Mass, Weight, and 

Gravity 

5.3 Forces in Equilibrium • Equilibrium 

Chapter 6: Laws of Motion 

6.1 Newton’s First Law • Net Force and 

Newton’s First Law 

6.2 Newton’s Second Law • Newton’s Second 

Law 

6.3 Newton’s Third Law and 

Momentum 

• Applying Newton’s 

Laws 

• Momentum 

• Momentum 

Conservation 

• Collisions and 

Conservation of 

Momentum 

• Isaac Newton 

• Gravity Problems 

• Universal 

Gravitation 

• Rate of Change of 

Momentum 

iii


Chapter 7: Work and Energy 

7.1 Force, Work, and 

Machines 

7.2 Energy and the 

Conservation of Energy 

iv 


• Mechanical 

Advantage 

• Mechanical 

Advantage of 

Simple Machines 

•Work 

• Types of Levers 

• Potential and 

Kinetic Energy 

• Identifying Energy 

Transformations 

• Energy 

Transformations 

Extra Practice 

• Conservation of 

Energy 

7.3 Efficiency and Power • Efficiency 

• Power 

Chapter 8: Matter and Temperature 

8.1 The Nature of Matter 

8.2 Temperature • Measuring 

Temperature 

• Temperature 

Scales 

8.3 Phases of Matter • Reading a Heating/ 

Cooling Curve 

• James Joule 

• Gear Ratios 

• Levers in the 

Human Body 

• Bicycle Gear Ratios 

Project 

• Power in Flowing 

Energy 

• Efficiency and 

Energy


Chapter 9: Heat 

9.1 Heat and Thermal 

Energy 


• Specific Heat 

Using the Heat 

Equation 

9.2 Heat Transfer Heat Transfer 

Chapter 10: Properties of Matter 

10.1 Density Measuring Mass 

with a Triple Beam 

Balance 

Measuring Volume 

Calculating Volume 

10.2 Properties of Solids 

Density 

10.3 Properties of Fluids Pressure in fluids 

Boyle’s Law 

10.4 Buoyancy Buoyancy 

Charles’ Law 

Pressure- 

Temperature 

Relationship 

Archimedes 

Narcis Monturiol 

Archimedes’ 

Principle 

v


Chapter 11: Weather and Climate 

11.1 Earth’s Atmosphere • Layers of the 

Atmosphere 

vi 


11.2 Weather Variables • Gaspard-Gustave 

Coriolis 

• Degree Days 

11.3 Weather Patterns • Joanne Simpson • Weather Maps 

Chapter 12: Atoms and the Periodic Table 

12.1 Atomic Structure • Structure of the 

Atom 

• Atoms and Isotopes 

12.2 Electrons • Electrons and 

Energy Levels 

12.3 The Periodic Table of 

the Elements 

12.4 Properties of the 

Elements 

Chapter 13: Compounds 

13.1 Chemical Bonds and 

Electrons 

13.2 Chemical Formulas • Finding the Least 

Common Multiple 

13.3 Molecules and Carbon 

Compounds 

• The Periodic Table 

• Dot Diagrams 

• Chemical Formulas 

• Naming 

Compounds 

• Ernest Rutherford 

• Neils Bohr 

• Tracking A 

Hurricane 

• Families of 

Compounds


Chapter 14: Changes in Matter 

14.1 Chemical Reactions • Chemical 

Equations 

14.2 Types of Reactions • Classifying 

Reactions 

14.3 Energy in Chemical 

Reactions 


14.4 Nuclear Reactions • Lise Meitner 

• Marie and Pierre 

Curie 

• Rosalyn Yalow 

• Chien-Shiung Wu 

Chapter 15: Matter and Earth’s Resources 

15.1 Chemical Cycles 

15.2 Global Climate Change • Svante Arrhenius 

• The Avogadro 

Number 

• Formula Mass 

• Predicting 

Chemical 

Equations 

• Percent Yield 

• Radioactivity 

vii


Chapter 16: Electricity 

16.1 Charge and Electric 

Circuits 

viii 


• Open and Closed 

Circuits 

16.2 Current and Voltage • Using an Electric 

Meter 

16.3 Resistance and Ohm’s 

Laws 

• Voltage, Current, 

and Resistance 

•Ohm’s law 

16.4 Types of Circuits •Series Circuits 

• Parallel Circuits 

Chapter 17: Magnetism 

17.1 Properties of Magnets • Magnetic Earth 

• Benjamin Franklin 

• Thomas Edison 

• George 

Westinghouse 

• Lewis Latimer 

17.2 Electromagnets • Maglev Train Model 

Project 

17.3 Electric Motors and 

Generators 

17.4 Generating Electricity • Michael Faraday • Transformers 

• Electrical Power


Chapter 18: Earth’s History and Rocks 


18.1 Geologic Time • Andrew Douglass 

18.2 Relative Dating • Relative Dating • Nicolas Steno 

18.3 The Rock Cycle • The Rock Cycle 

Chapter 19: Matter and Earth 

19.1 Inside Earth • Earth’s Interior • Charles Richter 

• Jules Verne 

19.2 Plate Tectonics • Alfred Wegener 

•Harry Hess 

• John Tuzo Wilson 

19.3 Plate Boundaries • Earth’s Largest 

Plates 

19.4 Metamorphic Rocks • Continental U.S. 

Geology 

Chapter 20: Earthquakes and Volcanoes 

20.1 Earthquakes • Averaging • Finding an 

Earthquake 

Epicenter 

20.2 Volcanoes • Volcano Parts 

20.3 Igneous Rocks • Basalt and Granite 

ix


Chapter 21: Water and Solutions 

21.1 Water 

21.2 Solutions • Concentration of 

Solutions 

• Solubility 

• Salinity and 

Concentration 

Problems 

x 


21.3 Acids, Bases, and pH • Calculating pH 

Chapter 22: Earth’s Water Systems 

22.1 Water on Earth’s 

Surface 

22.2 The Water Cycle • The Water Cycle 

22.3 Oceans 

Chapter 23: How Water Shapes the Land 

23.1 Weathering and 

Erosion 

23.2 Rivers, Streams, and 

Sedimentation 

23.3 Glaciers 

23.4 Sedimentary Rocks 

• Groundwater and 

Wells Project


Chapter 24: Waves and Sound 

24.1 Harmonic Motion • Period and 

Frequency 


• Harmonic Motion 

Graphs 

24.2 Properties of Waves • Waves • Wave Interference 

24.3 Sound • Decibel Scale 

• The Human Ear 

Chapter 25: Light and the Electromagnetic Spectrum 

25.1 Properties of Light • The 

Electromagnetic 

Spectrum 

• Standing Waves 

• Waves and Energy 

• Palm Pipes Project 

25.2 Color and Vision • Color Mixing • The Human Eye 

25.3 Optics • Measuring Angles • Using Ray 

Diagrams 

• Reflection 

• Refraction 

• Drawing Ray 

Diagrams 

xi


Chapter 26: The Solar System 

26.1 Motion in the Solar 

System 

26.2 Motion and 

Astronomical Cycles 

26.3 Objects in the Solar 

System 

Chapter 27: Stars 

xii 


• Astronomical Units 

Gravity Problems 

Universal 

Gravitation 

Touring the Solar 

System 

27.1 The Sun The Sun: 

A Cross-Section 

27.2 Stars Inverse Square 

Law 

27.3 Life Cycles of Stars 

Chapter 28: Exploring the Universe 

28.1 Tools of Astronomers Scientific Notation Understanding 

Light Years 

Parsecs 

Nicolaus 

Copernicus 

Galileo Galilei 

Johannes Kepler 

Benjamin Banneker 

Arthur Walker 

Edwin Hubble 

Measuring the 

Moon’s Diameter 

28.2 Galaxies Light Intensity Henrietta Leavitt Calculating 

Luminosity 

28.3 Theories About the 

Universe 

Doppler Shift

Name: Date: 

1.1 Lab Safety 

What can I do to protect myself and others in the lab? 

Science equipment and supplies are fun to use. 

However, these materials must always be used 

with care. Here you will learn how to be safe in 

a science lab. 

Follow these basic safety guidelines 

Your teacher will divide the class into groups. Each group should create a poster-sized display of one of the 

following guidelines. Hang the posters in the lab. Review these safety guidelines before each investigation. 

1. Prepare for each investigation. 

a. Read the investigation sheets carefully. 

b. Take special note of safety instructions. 

2. Listen to your teacher’s instructions before, during, and after the investigation. Take notes to help you 

remember what your teacher has said. 

3. Get ready to work: Roll long sleeves above the wrist. Tie back long hair. Remove dangling jewelry and any 

loose, bulky outer layers of clothing. Wear shoes that cover the toes. 

4. Gather protective clothing (goggles, apron, gloves) at the beginning of the investigation. 

5. Emphasize teamwork. Help each other. Watch out for one another’s safety. 

6. Clean up spills immediately. Clean up all materials and supplies after an investigation. 

Know what to do when... 

7. working with heat: 

a. Always handle hot items with a hot pad. Never use your bare hands. 

b. Move carefully when you are near hot items. Sudden movements could cause burns if you touch 

or spill something hot. 

c. Inform others if they are near hot items or liquids. 

8. working with electricity: 

Materials 

• Poster board 

• Felt-tip markers 

a. Always keep electric cords away from water. 

b. Extension cords must not be placed where they may cause someone to trip or fall. 

c. If an electrical appliance isn’t working, feels hot, or smells hot, tell a teacher right away. 

9. disposing of materials and supplies: 

a. Generally, liquid household chemicals can be poured into a sink. Completely wash the chemical 

down the drain with plenty of water. 

b. Generally, solid household chemicals can be placed in a trash can.

Page 2 of 6 

c. Any liquids or solids that should not be poured down the sink or placed in the trash have 

special disposal guidelines. Follow your teacher’s instructions. 

d. If glass breaks, do not use your bare hands to pick up the pieces. Use a dustpan and a brush to 

clean up. “Sharps” trash (trash that has pieces of glass) should be well labeled. The best way to 

throw away broken glass is to seal it in a labeled cardboard box. 

10. you are concerned about your safety or the safety of others: 

a. Talk to your teacher immediately. Here are some examples: 

• You smell chemical or gas fumes. This might indicate a chemical or gas leak. 

• You smell something burning. 

• You injure yourself or see someone else who is injured. 

• You are having trouble using your equipment. 

• You do not understand the instructions for the investigation. 

b. Listen carefully to your teacher’s instructions. 

c. Follow your teacher’s instructions exactly.

Page 3 of 6 

Safety quiz 

1. Draw a diagram of your science lab in the space below. Include in your diagram the following items. Include 

notes that explain how to use these important safety items. 

• Exit/entrance ways • Eye wash and shower • Sink 

• Fire extinguisher(s) • First aid kit • Trash cans 

• Fire blanket • Location of eye goggles • Location of 

and lab aprons 

special safety instructions 

2. How many fire extinguishers are in your science lab? Explain how to use them. 

3. List the steps that your teacher and your class would take to safely exit the science lab and the building in 

case of a fire or other emergency.

Page 4 of 6 

4. Before beginning certain investigations, why should you first put on protective goggles and 

clothing? 

5. Why is teamwork important when you are working in a science lab? 

6. Why should you clean up after every investigation? 

7. List at least three things you should you do if you sense danger or see an emergency in your classroom or 

lab. 

8. Five lab situations are described below. What would you do in each situation? 

a. You accidentally knock over a glass container and it breaks on the floor. 

b. You accidentally spill a large amount of water on the floor.

Page 5 of 6 

c. You suddenly you begin to smell a “chemical” odor that gives you a headache. 

d. You hear the fire alarm while you are working in the lab. You are wearing your goggles and lab apron. 

e. While your lab partner has her lab goggles off, she gets some liquid from the experiment in her eye. 

f. A fire starts in the lab. 

Safety in the science lab is everyone’s responsibility!

Page 6 of 6 

Safety contract 

Keep this contract in your notebook at all times. 

By signing it, you agree to follow all the steps necessary to be safe in your science class and lab. 

I, ____________________, (Your name) 

• Have learned about the use and location of the following: 

• Aprons and gloves 

• Eye protection 

• Eyewash fountain 

• Fire extinguisher and fire blanket 

• First aid kit 

• Heat sources (burners, hot plate, etc) and how to use them safely 

• Waste-disposal containers for glass, chemicals, matches, paper, and wood 

• Understand the safety information presented. 

• Will ask questions when I do not understand safety instructions. 

• Pledge to follow all of the safety guidelines that are presented on the Safety Skill Sheet at all times. 

• Pledge to follow all of the safety guidelines that are presented on investigation sheets. 

• Will always follow the safety instructions that my teacher provides. 

Additionally, I pledge to be careful about my own safety and to help others be safe. I understand that I am 

responsible for helping to create a safe environment in the classroom and lab. 

Signed and dated, 

______________________________ 

Parent’s or Guardian’s statement: 

I have read the Safety Skills sheet and give my consent for the student who has signed the preceding statement to 

engage in laboratory activities using a variety of equipment and materials, including those described. I pledge my 

cooperation in urging that she or he observe the safety regulations prescribed. 

____________________________________________________ _________________________________ 

Signature of Parent or Guardian Date

Name: Date: 

1.1 Using Your Textbook 

1.1 

Your textbook is a tool to help you understand and enjoy science. Colors, shapes, and symbols are used 

in the book to help you find information quickly. Take a few minutes to get familiar with these features—it will 

help you get the most out of your book all year long. 

Part 1: Organizing features of the student text 

Spend a few minutes answering the questions below. You will learn to recognize visual clues that organize the 

reading and help you find information quickly. 

1. What color is used to identify Unit four? 

2. List four important vocabulary words for section 3.2. 

3. What color are the boxes in which you found these vocabulary words? 

4. What is the main idea of the last paragraph on page 37? 

5. Where do you find section review questions? 

6. What is the first key question for Chapter 9? 

7. What are the four numbered parts (or steps) shown in each sample problem in the text? 

8. List the four sections of questions in each Chapter Assessment. 

Part 2: The Table of Contents 

The Table of Contents is found after the introduction pages. Use it to answer the following questions. 

1. How many units are in the textbook? List their titles. 

2. Which unit will be the most interesting to you? Why? 

3. Where do you find the glossary and index? How are they different? 

Part 3: Glossary and Index 

The glossary and index can help you quickly find information in your textbook. Use these tools to answer the 

following questions. 

1. What is the definition of velocity? 

2. On what pages will you find information about the layer of Earth’s atmosphere known as the troposphere? 

3. On what page will you find a short biography of agricultural scientist George Washington Carver?

Name: Date: 

1.1 SI Units 

In the late 1700's, as scientists began to develop the ideas of physics and chemistry, they needed better units of 

measurement to communicate scientific data. Scientists needed to prove their ideas with data based on 

measurements that other scientists could reproduce. A decimal system of units based on the meter as a standard 

length, the kilogram as a standard mass, and the liter as a standard volume was developed by the French. Today 

this system is known as the SI system, or metric system. 

The equations below show how the meter is related to other units in this system of measurements. 

1 meter = 100 centimeters 

1 cubic centimeter = 1 cm 3 = 1 milliliter 

1000 milliliters = 1 liter 

The SI system is easy to use because all the units are based on factors of 10. In 

the English system, there are 12 inches in a foot, 3 feet in a yard, and 5,280 feet 

in a mile. In the SI system, there are 10 millimeters in a centimeter, 

100 centimeters in a meter, and 1,000 meters in a kilometer. 

Question: Using the graphic at right, state how many kilometers it is from the 

North Pole to the equator. 

Answer: You need to convert 10,000,000 meters to kilometers. 

Since 1 meter = 0.001 kilometers, 0.001 is the multiplication factor. To solve, 

multiply 10,000,000 0.001 km = 10,000 km. So, it is 10,000 kilometers from 

the North Pole to the equator. 

These are the standard units of measurement that you will use in your scientific studies. The prefixes on the 

following page are used with the base units when measuring very large or very small quantities. 

When you are measuring: Use this standard unit: Symbol of unit 

mass kilogram kg 

length meter m 

volume liter l 

force newton N 

temperature degree Celsius °C 

time second s 

You may wonder why the kilogram, rather than the gram, is called the standard unit for mass. This is because the 

mass of an object is based on how much matter it contains as compared to the standard kilogram made from 

platinum and iridium and kept in Paris. The gram is such a small amount of matter that if it had been used as a 

standard, small errors in reproducing that standard would be multiplied into very large errors when large 

quantities of mass were measured. 

1.1

Page 2 of 3 

The following prefixes in the SI system indicate the multiplication factor to be used with the basic unit. 

For example, the prefix kilo- is a factor of 1,000. A kilometer is equal to 1,000 meters, and a kilogram is 

equal to 1,000 grams. 

Prefix kilo- hecto- deka- Basic unit 

(no prefix) 

deci- centi- milli- 

Symbol k h da m, l, g d c m 

Multiplication Factor 

or Place-Value 

1. How many centigrams are there in 24 grams? 

a. Restate the question: 24 grams = __________centigrams 

b. Use the place value chart to determine the multiplication factor, and solve: 

Since we want to convert grams (ones place) to centigrams 

(hundredths place), count the number of places on the chart 

it takes to move from the ones place to get to the hundredths 

place. Since it takes 2 moves to the right, the multiplication 

factor is 100. 

Solution: multiply 24 × 100 = 2,400. 

Answer: There are 2,400 centigrams in 24 grams. 

2. How many liters are there in 5,000 deciliters? 

a. Restate the question: 5,000 deciliters (dl) = __________ liters (l)? 


Since we want to convert deciliters (tenths place) to liters (ones 

place), count the number of places on the chart it takes to move 

from the ones place to get to the hundredths place. Since it 

takes 1 move to the left, the multiplication factor is 0.1. 

Solution: multiply 5,000 × 0.1 = 500. 

Answer: There are 500 liters in 5,000 deciliters. 

3. How many decimeters are in a dekameter? 

1,000 100 10 1 0.1 0.01 0.001 

kilo hecto deka meter, liter, or gram deci centi milli 

thousands hundreds tens ones tenths hundredths thousandths 

a. Restate the question: 1 dam =__________dm. 


1.1

Page 3 of 3 

Since we want to convert dekameters to decimeters, count 

the number of places on the chart it takes to move from the 

tens place (deka) to the tenths place (deci). It takes 2 

moves to the right, so the multiplication factor is 100. 

Solution: multiply 1 × 100 = 100. 

Answer: There are 100 decimeters in one dekameter. 

4. How many kilograms are equivalent to 520,000 centigrams? 

(1) Restate the question: 520,000 centigrams = __________ kilograms. 

(2) Determine the multiplication factor, and solve: 

Moving from the hundredths place (centi) to 

the thousands place (kilo) requires moving 5 

places to the left, so the multiplication factor is 

0.00001. 

Solution: Multiply 520,000 × 0.00001 = 5.2 

Answer: 5.2 kilograms are equivalent to 520,000 centigrams. 

1. How many grams are in a dekagram? 

2. How many millimeters are there in one meter? 

3. How many millimeters are in 6 decimeters? 

4. Convert 4,200 decigrams to grams. 

5. How many liters are equivalent to 500 centiliters? 

6. Convert 100 millimeters to meters. 

7. How many milligrams are equivalent to 150 dekagrams? 

8. How many liters are equivalent to 0.3 kiloliters? 

9. How many centimeters are in 65 kilometers? 

10. Twelve dekagrams are equivalent to how many milligrams? 

11. Seven hundred twenty centiliters is how many liters? 

12. A fountain can hold 53,000 deciliters of water. How many kiloliters is this? 

13. What is the name of a length that is 100 times larger than a millimeter? 

14. How many times larger than a centigram is a dekagram? 

15. Name the distance that is 10 times smaller than a centimeter. 

1.1

Name: Date: 

1.1 Scientific Notation 

1.1 

A number like 43,200,000,000,000,000,000 (43 quintillion, 200 quadrillion) can take a long time to 

write, and an even longer time to read. Because scientists frequently encounter very large numbers like this one 

(and also very small numbers, such as 0.000000012, or twelve trillionths), they developed a shorthand method 

for writing these types of numbers. This method is called scientific notation. A number is written in scientific 

notation when it is written as the product of two factors, where the first factor is a number that is greater than or 

equal to 1, but less than 10, and the second factor is an integer power of 10. Some examples of numbers written 

in scientific notation are given in the table below: 

Scientific Notation Standard Form 

4.32 × 10 19 43,200,000,000,000,000,000 

1.2 × 10 –8 0.000000012 

5.2777 × 10 7 52,777,000 

6.99 10 -5 0.0000699 

Rewrite numbers given in scientific notation in standard form. 

• Express 4.25 × 10 6 in standard form: 4.25 × 10 6 = 4,250,000 

Move the decimal point (in 4.25) six places to the right. The exponent of the “10” is 6, giving us the number 

of places to move the decimal. We know to move it to the right since the exponent is a positive number. 

• Express 4.033 × 10 –3 in standard form: 4.033 × 10 –3 = 0.004033 

Move the decimal point (in 4.033) three places to the left. The exponent of the “10” is negative 3, giving the 

number of places to move the decimal. We know to move it to the left since the exponent is negative. 

Rewrite numbers given in standard form in scientific notation. 

• Express 26,040,000,000 in scientific notation: 26,040,000,000 = 2.604 × 10 10 

Place the decimal point in 2 6 0 4 so that the number is greater than or equal to one (but less than ten). This 

gives the first factor (2.604). To get from 2.604 to 26,040,000,000 the decimal point has to move 10 places to 

the right, so the power of ten is positive 10. 

• Express 0.0001009 in scientific notation: 0.0001009 = 1.009 × 10 –4 


gives the first factor (1.009). To get from 1.009 to 0.0001009 the decimal point has to move four places to 

the left, so the power of ten is negative 4.

Page 2 of 3 

1. Fill in the missing numbers. Some will require converting scientific notation to standard form, 

while others will require converting standard form to scientific notation. 

a. 6.03 × 10 –2 

b. 9.11 × 10 5 

c. 5.570 × 10 –7 


d. 999.0 

e. 264,000 

f. 761,000,000 

g. 7.13 × 10 7 

h. 0.00320 

i. 0.000040 

j. 1.2 × 10 –12 

k. 42,000,000,000,000 

l. 12,004,000,000 

m. 9.906 × 10 –2 

2. Explain why the numbers below are not written in scientific notation, then give the correct way to write the 

number in scientific notation. 

Example: 0.06 × 10 5 is not written in scientific notation because the first factor (0.06) is not greater than or 

equal to 1. The correct way to write this number in scientific notation is 6.0×103 . 

a. 2.004 × 111 b. 56 × 10 –4 

c. 2 × 100 2 

d. 10 × 10 –6 

1.1

Page 3 of 3 

3. Write the numbers in the following statements in scientific notation: 

a. The national debt in 2005 was about $7,935,000,000,000. 

b. In 2005, the U.S. population was about 297,000,000 

c. Earth's crust contains approximately 120 trillion (120,000,000,000,000) metric tons of gold. 

d. The mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 91 kilograms. 

e. The usual growth of hair is 0.00033 meters per day. 

f. The population of Iraq in 2005 was approximately 26,000,000. 

g. The population of California in 2005 was approximately 33,900,000. 

h. The approximate area of California is 164,000 square miles. 

i. The approximate area of Iraq in 2005 was 169,000 square miles. 

j. In 2005, one right-fielder made a salary of $12,500,000 playing professional baseball. 

1.1

Name: Date: 

1.2 Measuring Length 

How do you find the length of an object? 

Size matters! When you describe the length of an 

object, or the distance between two objects, you 

are describing something very important about the 

object. Is it as small as a bacteria (2 micrometers)? 

Is it a light year away (9.46 × 10 15 meters)? By 

using the metric system you can quickly see the 

difference in size between objects. 

Reading the meter scale correctly 

Look at the ruler in the picture above. Each small line on the top of the ruler represents one millimeter. Larger 

lines stand for 5 millimeter and 10 millimeter intervals. When the object you are measuring falls between the 

lines, read the number to the nearest 0.5 millimeter. Practice measuring several objects with your own metric 

ruler. Compare your results with a lab partner. 

Stop and think 

Materials 

• Metric ruler 

• Pencil 

• Paper 

• Small objects 

• Calculator 

a. You may have seen a ruler like this marked in centimeter units. How many millimeters are in one 

centimeter? 

b. Notice that the ruler also has markings for reading the English system. Give an example of when it would 

be better to measure with the English system than the metric system. Give a different example of when it 

would be better to use the metric system.

Page 2 of 4 

Example 1: Measuring objects correctly 

Look at the picture above. How long is the building block? 

1. Report the length of the building block to the nearest 0.5 millimeters. 

2. Convert your answer to centimeters. 

3. Convert your answer to meters. 


Look at the picture above. How long is the pencil? 

1. Report the length of the pencil to the nearest 0.5 millimeters. 

2. Challenge: How many building blocks in example 1 will it take to equal the length of the pencil? 

3. Challenge: Convert the length of the pencil to inches by dividing your answer by 25.4 millimeters per inch.

Page 3 of 4 


Look at the picture above. How long is the domino? 

1. Report the length of the domino to the nearest 0.5 millimeters. 

2. Challenge: How many dominoes will fit end to end on the 30 cm ruler? 

Practice converting units for length 

By completing the examples above you show that you are familiar with some of the prefixes used in the metric 

system like milli- and centi-. The table on the following page gives other prefixes you may be less familiar with. 

Try converting the length of the domino from millimeters into all the other units given in the table. 

Refer to the multiplication factor this way: 

• 1 kilometer equals 1000 meters. 

• 1000 millimeters equals 1 meter. 

1. How many millimeters are in a kilometer? 

1000 millimeters per meter × 1000 meters per kilometer = 1,000,000 millimeters per kilometer 

2. Fill in the table with your multiplication factor by converting millimeters to the unit given. The first one is 

done for you. 

1000 millimeters per meter × 10 –12 meters per picometer = 10 –9 millimeters per picometer 

3. Divide the domino’s length in millimeters by the number in your multiplication factor column. This is the 

answer you will put in the last column. 

42.5 millimeters ÷ 10 –9 millimeters per picometer = 42.5 ×10 9 picometers

Page 4 of 4 

4. . 

Prefix Symbol Multiplication 

factor 

Scientific notation 

in meters 

Your multiplication 

factor 

Your domino 

length in: 

pico- p 0.000000000001 10 –12 10 –9 42.5 ×10 9 pm 

nano- n 0.000000001 10 –9 nm 

micro- µ 0.000001 10 –6 μm 

milli m 0.001 10 –3 

centi- c 0.01 10 –2 

deci- d 0.1 10 –1 

deka- da 10 10 1 

hecto- h 100 10 2 

kilo- k 1000 10 3 

mm 

cm 

dm 

dam 

hm 

km

Name: Date: 

1.2 Averaging 

The most common type of average is called the mean. Usually when someone (who’s not your math teacher) asks 

you to find the average of something, it is the mean that they want. To find the mean, just sum (add) all the data, 

then divide the total by the number of items in the data set. This type of average is used daily by many people. 

Teachers and students use it to average grades. Meteorologists use it to average normal high and low 

temperatures for a certain date. Sports statisticians use it to calculate batting averages and many other things. 

• William has had three tests so far in his English class. His grades are 80%, 75%, and 90%. What is his 

average test grade? 

Solution: 

a. Find the sum of the data: 80 + 75 + 90 = 245 

b. Divide the sum (245) by the number of items in the data set (3): 245 ≥ 3 ≈ 82% 

William’s average (mean) test grade in English (so far) is about 82% 

1. The families on Carvel Street were cleaning out their basements and garages to prepare for their annual 

garage sale. At 202 Carvel Street, they found seven old baseball gloves. At 208, they found two baseball 

gloves. At 214, they found four gloves, and at 221 they found two gloves. If these are the only houses on the 

street, what is the average number of old baseball gloves found at a house on Carvel Street? 

2. During a holiday gift exchange, the members of the winter play cast set a limit of $10 per gift. The actual 

prices of each gift purchased were: $8.50, $10.29, $4.45, $12.79, $6.99, $9.29, $5.97, and $8.33. What was 

the average price of the gifts? 

3. During weekend baby sitting jobs, each sitter charged a different hourly rate. Rachel charged $4.00, Juanita 

charged $3.50, Michael charged $4.25, Rosa charged $5.00, and Smith charged $3.00. 

a. What was the average hourly rate charged among these baby sitters? 

b. If they each worked a total of eight hours, what was their average pay for the weekend? 

4. The boys on the ninth grade basketball team at Fillmore High School scored 22 points, 12 points, 8 points, 4 

points, 4 points, 3 points, 2 points, 2 points, and 1 point in Thursday’s game. What was the average number 

of points scored by each player in the game? 

5. Jerry and his friends were eating pizza together on a Friday night. Jerry ate a whole pizza (12 slices) by 

himself! Pat ate three slices, Jack ate seven slices, Don and Dave ate four slices each, and Teri ate just two 

slices. What was the average number of slices of pizza eaten by one of these friends that night? 

1.2

Name: Date: 

1.2 Reading Strategies (SQ3R) 

Students often read a science textbook as if they were watching a movie—they just sit there and expect to take it 

all in. Actually, reading a science book is more like playing a video game. You have to interact with it! This skill 

builder will teach you active strategies that will improve your reading and study skills. Remember—just like in 

video game playing—the more you practice these strategies, the more skilled you will become. 

The SQ3R active reading method was developed in 1941 by Francis Robinson to help his students get the most 

out of their textbooks. Using the SQ3R method will help you interact with your text, so that you understand and 

remember what you read. “SQ3R” stands for: 

Survey 

Question 

Read 

Recite 

Review 

Your student text has many features to help you organize your reading. These features are highlighted in 

Chapter 1: Measurement, found on pages 3–32 of your student text. Open your text to those pages so that you 

can see the features for yourself. 

Survey the chapter first. 

• Skim the introduction on the first page of every chapter. Notice the key questions. The key questions are 

thought-provoking and designed to spark your interest in the chapter. See if you can answer these questions 

after you have read the entire chapter. 

• You will find vocabulary words with their definitions in blue boxes on the right side of each page. 

Vocabulary words will be scattered throughout the chapter. Write down any vocabulary words that are 

unfamiliar to you to help you recognize them later. 

• Next, skim the chapter to get an overview. Notice the section numbers and titles. These divide the chapter 

into major topics. The subheadings in each section outline important points. Vocabulary words are 

highlighted in bold blue type. Solving Problems pages provide step-by-step examples to help you learn to 

use mathematical formulas. Tables, charts, and figures summarize important information. 

• Read the section review questions at the end of each section. The questions help you identify what you are 

expected to know when you finish your reading. You will also find Challenge, Solve It, Study Skills, 

Journal, Science Fact, and/or Technology boxes scattered throughout each section. These boxes provide you 

with an interesting way to learn more about information in the section. 

• Carefully read the Chapter Assessment at the end of the chapter to see what kinds of questions you will need 

to be able to answer. Notice that it is divided into four subtitles: Vocabulary, Concepts, Problems, and 

Applying Your Knowledge. Each set is listed by chapter section. 

1.2

Page 2 of 2 

Question what you see. Turn headings into questions. 

• Look at each of the section headings and subheadings, found at the tops of pages in your text. 1.2 

Change each heading to a question by using words such as who, what, when, where, why, and how. 

For example, Section 1.1: Measurements could become What measurements will I need to make in physical 

science? The subheading Two common measurement systems could become What are two common 

measurement systems? Write down each question and try to answer it. Doing this will help you pinpoint 

what you already know and what you need to learn as you read. 

Read and look for answers to the questions you wrote. 

• Pay special attention to the sidenotes in the left margin of each page. For example, under the Section 1.3 

subheading Converting between English and SI units, the sidenotes are: The problem of multiple units 

and Comparing English and SI units. These phrases and short sentences are designed to guide you to the 

main idea of each paragraph. Also, note the sidebars and illustrations on the right side of the page with 

additional explanations and concepts. For example, the target diagrams in Figure 1.4 will help you 

understand the terms accuracy, precision, and resolution. 

• Slow your reading pace when you come to a difficult paragraph. Read difficult paragraphs out loud. Copy a 

confusing sentence onto paper. These methods force you to slow down and allow you time to think about 

what the author is saying. 

Recite concepts out loud. 

• This step may seem strange at first, because you are asked to talk to yourself! But studies show that saying 

concepts out loud can actually help you to record them in your long-term memory. 

• At the end of each section, stop reading. Ask yourself each of the questions you wrote in step two on the 

previous page. Answer each question out loud, in your own words. Imagine that you are explaining the 

concept to someone who hasn’t read the text. 

• You may find it helpful to write down your answers. By using your senses of seeing, hearing, and touch 

(when you write), you create more memory paths in your brain. 

Review it all. 

• Once you have finished the entire chapter, go back and answer all of the questions that you wrote for each 

section. If you can’t remember the answer, go back and reread that portion of the text. Recite and write the 

answer again. 

• Next, reread the key questions at the beginning of the chapter. Can you answer these? 

• Complete the section reviews and the chapter assessment. Use the glossary and index at the back of the book 

to help you locate specific definitions. 

The SQ3R method may seem time-consuming, but it works! With practice, you will learn to recognize the 

important concepts quickly. 

Active reading helps you learn and remember what you have read, so you will have less to re-learn as you study 

for quizzes and tests.

Name: Date: 

1.2 Stopwatch Math 

What do horse racing, competitive swimming, stock car racing, speed skating, many track and field events, and 

some scientific experiments have in common? The need for some sort of stopwatch, and people to interpret the 

data. For competitive athletes in speed-related sports, finishing times (and split times taken at various intervals of 

a race) are important to help the athletes gauge progress and identify weaknesses so they can adjust their training 

and improve their performance. 

• Three girls ran the following times for one mile in their gym class: Julie ran 9:33.2 (9 minutes, 

33.2 seconds), Maggie ran 9:44.24 (9 minutes, 44.24 seconds), and Mel ran 9:33.27 (9 minutes, 

33.27 seconds). In what order did they finish? 

Solution: 

The girl who came in first is the one with the fastest (smallest) time. Compare each time digit by digit, 

starting with the largest place-value. Here, that would be the minutes place: 

There is a “9” in the minutes’ place of each time, so next, compare the seconds’ place. Since Maggie’s time 

has larger numbers in the seconds’ place (44) than Julie or Mel (33), her time is larger (slower) than the 

other two. We know Maggie finished third out of the three girls. Now, comparing Julie’s time (9:33.2) to 

Mel’s (9:33.27), it is helpful to rewrite Julie’s time (9:33.2) so that it has the same number of places as 

Mel’s. Julie’s time needs one more digit, so adding a zero onto the end of her time, it becomes 9:33.20. 

Notice that Mel’s time is larger (slower) than Julie’s (27 > 20). This means that Julie’s time was fastest 

(smallest), so she finished first, followed by Mel, and Maggie’s time was the slowest (largest). 

1. Put each set of times in order from fastest to slowest. 

a. 5.5 5.05 5 5.2 5.15 

Fastest Slowest 

b. 6:06.04 6:06 6:06.4 6:06.004 


1.2

Page 2 of 2 

2. The table below gives the winners and their times from eight USA track and field championship 

races in the men’s 100 meter run. Rewrite the table so that the times are in order from fastest to 

slowest. Include the times and the years. Please note that the “w” that occurs next to some times 

indicates that the time was wind aided. 

Year 2005 2004 2003 2002 2001 2000 1999 1998 

Time 10.08 9.91 10.11 9.88w 9.95w 10.01 9.97w 9.88w 

Name Justin 

Gatlin 

Time 

Year 

Maurice 

Greene 

Bernard 

Williams 

Maurice 

Greene 

Tim 

Montgomery 

Maurice 

Greene 

3. The following times were recorded during an experiment with battery-powered cars. Put them in order from 

fastest to slowest. 

a. 1:22.4 1:24.007 1:25 1:22.04 1:23.117 1:23.2 1:24 1:33 

b. 1:18.3 1:20.22 1:21.003 1:20 1:17.99 1:21.2 1:18.22 

c. 1:25 1:24.99 1:24.099 1:25.001 1:24.9901 1:24.9899 

Dennis 

Mitchell 

Tim 

Harden 




4. Write a set of five times (in order from fastest to slowest) that are all between 26:15.2 and 26:15.24. Do 

not include the given numbers in your set. 

1.2

Name: Date: 

1.2 Understanding Light Years 

1.2 

How far is it from Los Angeles to New York? Pretty far, but it can still be measured in miles or 

kilometers. How far is it from Earth to the Sun? It’s about one hundred forty-nine million, six hundred thousand 

kilometers (149,600,000, or 1.496 × 108 km). Because this number is so large, and many other distances in space 

are even larger, scientists developed bigger units in order to measure them. An Astronomical Unit (AU) is 

1.496 × 108 km (the distance from Earth to the sun). This unit is usually used to measure distances within our 

solar system. To measure longer distances (like the distance between Earth and stars and other galaxies), the light 

year (ly) is used. A light year is the distance that light travels through space in one year, or 9.468 × 1012 km. 

1. Converting light years (ly) to kilometers (km) 

Earth’s closest star (Proxima Centauri) is about 4.22 light years away. How far is this in kilometers? 

Explanation/Answer: Multiply the number of kilometers in one light year (9.468 × 1012 km/ly) by the 

number of light years given (in this case, 4.22 ly). 

2. Converting kilometers to light years 

Polaris (the North Star) is about 4.07124 × 10 15 km from the earth. How far is this in light years? 

Explanation/Answer: Divide the number of kilometers (in this case, 4.07124 × 10 15 km) by the number of 

kilometers in one light year (9.468 × 1012 km/ly). 

Convert each number of light years to kilometers. 

1. 6 light years 

2. 4.5 × 10 6 light years 

3. 4 × 10 –3 light years 

Convert each number of kilometers to light years. 

4. 5.06 × 10 16 km 

5. 11 km 

4.07124 10 15 × km 

6. 11,003,000,000,000 km 

9.468 10 12 

( 

-------------------------------------------- 

× ) km 

× 4.22 ly 3.995 10 

1 ly 

13 ≈ × km 

9.468 10 12 × km 4.07124 10 

÷ --------------------------------------- 

1 ly 

15 × km 1 ly 

--------------------------------------------- 

1 9.468 10 12 = × --------------------------------------- ≈ 

430 light years 

× km

Page 2 of 2 

Solve each problem using what you have learned. 

7. The second brightest star in the sky (after Sirius) is Canopus. This yellow-white supergiant 

is about 1.13616 × 10 16 kilometers away. How far away is it in light years? 

8. Regulus (one of the stars in the constellation Leo the Lion) is about 350 times brighter than the sun. It is 

85 light years away from the earth. How far is this in kilometers? 

9. The distance from earth to Pluto is about 28.61 AU from the earth. Remember that an AU = 1.496 × 108 km. 

How many kilometers is it from Pluto to the earth? 

10. If you were to travel in a straight line from Los Angeles to New York City, you would travel 

3,940 kilometers. How far is this in AU’s? 

11. Challenge: How many AU’s are equivalent to one light year? 

1.2

Name: Date: 

1.2 Indirect Measurement 

Have you ever wondered how scientists and engineers measure large quantities like the mass of an iceberg, the 

volume of a lake, or the distance across a river? Obviously, balances, graduated cylinders, and measuring tapes 

could not do the job! Very large (or very small) quantities are calculated through a process called indirect 

measurement. This skill sheet will give you an opportunity to try indirect measurement for yourself. 

• The length of a tree’s shadow is 4.25 meters and the length of a meter stick’s shadow is 1.25 meters. Using 

these two values and the length of the meter stick, how tall is the tree? 

Looking for 

The height of a tree. 

Given 

Tree’s shadow = 4.25 m 

Meter’s stick’s shadow = 1.25 m 

Height of meter stick = 1 m 

Relationships 

There is a direct relationship between the height of 

objects and the length of their shadows. 

height of meter stick height of object 

= 

length of meter stick shadow length of object shadow 

Solution 

The height of the tree is 3.40 meters. 

• At the science museum, 12 first graders stand on a giant scale to measure their mass. The combined mass of 

the 12 first graders is 262 kilograms. What is the average mass of a first grader in this group? 

Looking for 

The average mass of a first grader. 

Given 

Total mass of 12 first graders = 262 kilograms 

Relationships 

To get the average mass of one first grader, divide the 

total mass by 12. 

262 kilograms 

12 

1.00 m height of tree 

= 

1.25 m 4.25 m 

1.00 m height of tree 

4.25 m× = × 4.25 m 

1.25 m 4.25 m 

3.40 m = height of tree 

Solution 

262 kilograms 

= 21.8 kilograms 

12 

The average mass of a first grader in this 

group is 21.8 kilograms. 

1. You go to another forest and measure the shadow of a tree to be 6 meters long. The shadow of your meter 

stick is 2 meters long. How tall is the tree? 

2. The height of a flagpole is 8.50 meters. If the length of the meter stick shadow is 1.50 meters, what is the 

length of the flagpole’s shadow? 

1.2

Page 2 of 2 

3. While touring a city, you see a skyscraper and wonder how tall it is. You see that it is clearly 

divided into floors. You estimate that each floor is 20. feet high. You count that the skyscraper has 

112 floors. 

a. Approximately how tall is this skyscraper in feet? 

b. Approximately how tall is the skyscraper in meters? (One foot is about 0.3 meter.) 

4. There are 10 apples in a one-kilogram bag of apples. What is the average mass of each apple in the bag? 

Give your answer in units of kilograms and grams. 

5. If you place one staple on an electronic balance, the balance still reads 0.00 grams. However, if you place 

210 staples on the balance, it reads 6.80 grams. What is the mass of one staple? 

6. A stack of 55 business cards is 1.85 cm tall. Use this information to determine the thickness of one business 

card. 

7. A stack of eight compact disks is 1.0 centimeter high. What is the thickness of one compact disk (CD) in 

centimeters? What is the thickness of one CD in millimeters? 

8. A quarter is 2.4 millimeters thick. How tall are the following stacks of quarters? 

a. A stack worth 50 cents 

b. A stack worth $1 

c. A stack worth $5 

d. A stack worth $1,000 

(Give your answer in millimeters and meters.) 

9. Yvonne has gained a reputation for her delicious cheesecakes. She takes orders for 10 cheesecakes and 

spends 8.5 hours on one Saturday baking them all. She earns $120 from selling these cheesecakes. 

a. What is the average length of time to make one cheesecake? Give your answer in minutes. 

b. What does Yvonne charge for each cheesecake? 

c. How much money is Yvonnne earning per hour for her work? 

10. A sculptor wants to create a statue. She goes to a quarry to buy a block of marble. She finds a chip of marble 

on the ground. The volume of the chip is 15.3 cm 3 . The mass of the chip is 41.3 grams. The sculptor 

purchases a block of marble 30.0-by-40.0-by-100.0 cm. Use a proportion to find the mass of her block of 

marble. 

11. The instructions on a bottle of eye drops say to place three drops in each eye, using the dropper. How could 

you find the volume of one of these drops? Write a procedure for finding the volume of a drop that includes 

using a glass of water, a 10.0-mL graduated cylinder, and the dropper. 

12. A student wants to use indirect measurement to find the thickness of a 

sheet of newspaper. In a 50-centimeter tall recycling bin, she finds 50 

sheets of newspaper. Each sheet in the bin is folded in fourths. Design a 

procedure for the student to use that would allow her to measure the 

thickness of one sheet of newspaper with little experimental error. The 

student has a meter stick and a calculator. 

1.2

Name: Date: 

1.3 Dimensional Analysis 

Dimensional analysis is a way to find the correct label (also called units or dimensions) for the solution to a 

problem. In dimensional analysis, we treat the units the same way that we treat the numbers. For example, this 

problem shows how can you can “cancel” the sevens and then perform the multiplication: 

3 7 

-- • -- 

7 8 

In some problems, there are no numerical cancellations to make, but you need to pay close attention to the units 

(or dimensions): 

• If there are 16 ounces in one pound, how many ounces are in four pounds? 

16 oz 

------------ • 4 lb 

1 lb 

= 

16 • 4 oz • lb 

------------------------------- 

1 lb 

= 

64 oz 

------------ 

1 

= 64 oz 

The “lbs” may be cancelled either before or after the multiplication. 

The goal of dimensional analysis is to simplify a problem by focusing on the units of measurement (dimensions). 

Dimensional analysis is very useful when converting between units (like converting inches to yards, or 

converting between the English and SI systems of measurement). 

• The ninth grade class is having a reward lunch for collecting the most food for a canned food drive. They 

have decided to order pizza. They are figuring two slices of pizza per student. Each pizza that will be ordered 

will have 12 slices. There are 220 students total in the ninth grade. How many pizzas should they order? 

Solution: 

1. Determine what we want to find out: here, it is the number or whole pizzas needed to feed 220 ninth graders. 

It’s important to remember that if the solution is to have the label “pizzas,” “pizzas” should be kept in the 

numerator as the problem is set up. 

2. Determine what we know. We know that they’re planning 2 slices of pizza per student, that there are 

12 slices in each pizza, and that there are 220 ninth graders. 

2 

3. Write what you know as fractions with units. Here, we have: ----------------slices 

12 

, -------------------slices 

and 220 students. 

student pizza 

= 

12 

Notice that in the fraction, -------------------slices 

, “pizza” is in the denominator. 

pizza 

Recall that (from step #1, above) “pizza” should be kept in the numerator, as it will be the label of the final 

solution. To correct this problem, just switch the numerator and denominator: -------------------- 

1 pizza 

. 

12 slices 

3 

-- 

8 

1.3

Page 2 of 2 

4. Set up the problem by focusing on the units. Just writing the information as a multiplication 

problem, we have: 

5. Calculate: 

Therefore, 37 pizzas will need to be ordered. 

Notice that canceling the units can be done either before or after the multiplication. 

6. Check your solution for reasonableness: Since there are 12 slices in each pizza, and we’re figuring that each 

student will eat 2 slices, one pizza will feed 6 students. It is expected that a little less than 40 pizzas would be 

needed. It does seem reasonable that 37 pizzas would feed 220 students. 

1. Multiply. Be sure to label your answers. 

a. 

b. 

$12.00 

--------------- 

6 hr 

• ------------- 

1 hr 1 day 

------------------- 

2 lbs 

1 person 

-------------------- 

1 pizza 

12 slices 

7 days 

• ---------------- 

1 week 

• 

-------------------- 

1 pizza 

12 slices 

2 

----------------slices 

220 students 

• ----------------------------student 

1 

15 people 

• 

---------------------- 

1 day 

• 

2 

----------------slices 

220 students 

• ----------------------------student 

1 

110 

-----------------------------------------------------------------pizza 

• slices • students 

36 

3 slices • students 

2 

= = -- pizzas 

3 

2. Use dimensional analysis to convert each. You may need to use a reference to find some conversion factors. 

Show all of your work. 

a. 11.0 quarts to some number of gallons 

b. 220. centimeters to some number of meters 

c. 6000. inches to some number of miles 

d. How many cups are there in 4.0 gallons? 

3. Use dimensional analysis to find each solution. You may need to use a reference to find some conversion 

factors. Show all of your work. 

a. Frank just graduated from eighth grade. Assuming exactly four years from now he will graduate from 

high school, how many seconds does he have until his high school graduation? 

b. In 2005, Christian Cantwell won the US outdoor track and field championship shot put competition with 

a throw of 21.64 meters. How far is this in feet? 

c. A recipe for caramel oatmeal cookies calls for 1.5 cups of milk. Sam is helping to make the cookies for 

the soccer and football teams plus the cheerleaders and marching band, and needs to multiply the recipe 

by twelve. How much milk (in quarts) will he need altogether? 

d. How many football fields (including the 10 yards in each end zone) would it take to make a mile? 

e. Corey’s sister’s car gets 30. miles on each gallon of gas. How many kilometers per gallon is this? 

f. Convert your answer from (e) to kilometers per liter. 

g. A car is traveling at a rate of 65 miles per hour. How many feet per second is this? 

1.3

Name: Date: 

Skill Builder Fractions Review 

1.3 Fractions Review 

In physical science classes, you will solve problems that involve fractions. Understanding the rules for addition, 

subtraction, multiplication, and division of fractions helps you solve these problems. The diagram below shows 

the parts of a fraction. This skill sheet guides you through a review of the rules for working with fractions. You 

will see how the rules are used in both simple and complex fractions. 

Addition and subtraction of fractions 

To add or subtract fractions you must first have a common denominator. For example, if you wanted to add or 

subtract 5 / 8 and 6 / 4 , you must first convert both denominators to the same number. 

Addition: 

Subtraction: 

As you can see, the rules for adding and subtracting positive and negative numbers also apply to fractions. 

Multiplication of fractions 

5 6 5 ⎛26⎞ 5 12 17 

+ = + ⎜ × ⎟= 

+ = 

8 4 8 ⎝2 4⎠ 8 8 8 

5 6 5 ⎛2 6⎞ 5 12 −7 

− = − ⎜ × ⎟= 

− = 

8 4 8 ⎝2 4⎠ 8 8 8 

To multiply fractions, first multiply the numerators and then multiply the denominators. For example: 

5 6 30 

× = 

8 4 32 

Fractions are commonly expressed in their lowest terms so that they are easier to recognize. To find a fraction’s 

lowest terms, you need to divide the numerator and the denominator by any common factors. The fraction in the 

example above can be rewritten like this: 

30 3× 2× 5 

= 

32 2× 2× 2× 2 

1.3

Page 2 of 4 

This form is called the prime factorization because all of the factors are prime numbers (this means they 

can’t be divided by any whole number except 1 to get a whole number answer). Notice that there’s a 2 

in both the numerator and the denominator. Cross out any factor that appears in both places. Multiply 

out the remaining factors. The simplified fraction is: 

At other times you may be asked to change the fraction to a decimal. This is very easy! Simply divide the 

numerator by the denominator. Remember that the divisor line between the numerator and the denominator in a 

fraction means “divide by” and is the same as a division sign (÷). 

Division of fractions 

To divide fractions you first invert (turn upside down) the second fraction and then multiply. Follow the rules for 

multiplying fractions. When necessary, reduce the fraction to its lowest terms. For example: 

Division of complex fractions 

An example of a complex fraction is shown below. A complex fraction is a fraction of fractions. You can divide 

complex fractions using the rules you already know for dividing fractions. For example: 

Reduce: 

3× 5 15 

= 

2× 2× 2× 2 32 

30 

= 30 ÷ 32 = 0.9375 

32 

5 6 5 4 20 

÷ = × = 

8 4 8 6 48 

20 2× 2× 5 5 5 

= = = 

48 2× 2× 2× 2× 3 2× 2× 3 12 

5 

8 ⎛5 6⎞ 5 4 20 

= 

6 ⎜ ÷ ⎟= 

× = 

⎝8 4⎠ 8 6 48 

4 

20 2× 2× 5 5 

= = 

48 2× 2× 2× 2× 3 12 

As you can see, the last two examples yielded the same answer. Can you see why? The two examples are the 

same, but written differently. The line between the two fractions, 5 / 8 and 6 / 4, acts the same as a division (≥) sign. 

1.3

Page 3 of 4 

Solving fraction problems 

Now it’s your turn to solve some problems. Be sure to show your work. Reduce your answers to lowest terms. 

Addition of fractions: 

1. 

2. 

3. 

4. Express the above fractions in decimal form. 

Subtraction of fractions: 

4 

1. ----- 

12 

3 

– -- 

4 

2. 

3. 


Multiplication of fractions: 

1. ----- 

4 

12 

3 

× -- 

4 

2. 

3. 

----- 

4 

+ 

3 

-- 

12 4 

7 5 

-- + -- 

8 7 

3 6 5 

-- + -- + -- 

4 8 3 

7 

-- 

8 

5 

– -- 

7 

3 

-- 

4 

6 5 

– -- – -- 

8 3 

7 

-- 

8 

5 

× -- 

7 

3 

-- 

4 

6 5 

× -- × 

-- 

8 3 


1.3

Page 4 of 4 

Division of fractions: 

1. 

2. 

3. 

4. 


Division of complex fractions: 

1. 

2. 

3. 

4. 

----- 

4 

12 

3 

÷ -- 

4 

7 

-- 

8 

5 

÷ -- 

7 

10 1 

----- ÷ -- 

15 3 

8 2 

----- ÷ -- 

18 3 

3 

-- 

4 

6 

-- 

8 

3 

-- 

4 

5 

-- 

3 

7 

× -- 

6 

5 

-- 

-------------- 

3 

10 

----- 

2 

× -- 

4 3 

25 

----- 

-------------- 

10 

15 

----- 

5 

÷ -- 

3 3 


1.3

Name: Date: 

1.3 Significant Digits 

Francisco is training for a 10-kilometer run. Each morning, he runs a loop around his neighborhood. To find out 

exactly how far he’s running, he asks his older sister to drive the loop in her car. Using the car’s trip odometer, 

they find that the route is 7.2 miles long. 

To find the distance in kilometers, Francisco looks in the reference 

section of his science text and finds that 1.000 mile = 

1.609 kilometers. He multiplies 7.2 miles by 1.609 km/mile. The 

answer, according to his calculator, is 11.5848 kilometers. 

Francisco wonders what all those numbers after the decimal point 

really mean. Can a car odometer measure distances as small as 0.0008 

kilometer? That’s a distance less than one meter! 

This skill sheet will help you answer Francisco’s question. It will also 

help you figure out which digits in your own calculations are 

significant. 

What are significant digits? 

Significant digits are the meaningful digits in a measured quantity. Scientists have agreed upon a number of rules 

to determine which numbers in a measurement are significant. The rules are: 

1. Non-zero digits in a measurement are always significant. This means that the distance measured by the 

car odometer, 7.2 miles, has two significant digits. 

2. Zeros between two significant digits in a measurement are significant. This means that the measurement 

of kilometers per mile, 1.609 kilometers, has four significant digits. 

3. All final zeros to the right of a decimal point in a measurement are significant. This means that the 

measurement 1.000 miles has four significant digits. 

4. If there is no decimal point, final zeros in a measurement are NOT significant. This means that the 

number 20 in the phrase “20-liter water cooler” has one significant digit. The water cooler isn’t marked off 

in 1-liter increments, so no measurement decision was made regarding the ones place. 

5. A decimal point is used after a whole number ending in zero to indicate that a final zero IS significant. 

If you measure 100 grams of lemonade powder to the nearest whole gram, write the number as 100. grams. 

This shows that your measurement has three significant digits. 

6. In a measurement, zeros that exist only to put the decimal point in the right place are NOT significant. 

This means that the number 0.0008 in the phrase “0.0008 kilometer” has one significant digit. 

7. A number that is found by counting rather than measuring is said to have an infinite number of 

significant digits. For example, the race officials count 386 runners at the starting line. The number 386, in 

this case, has an infinite number of significant digits. 

1.3

Page 2 of 4 

Find the number of significant digits 

Table 1: Number of Significant Digits 

Value How many significant digits does each value have? 

a. 36.33 minutes 

b. 100 miles 

c. 120.2 milliliters 

d. 0.0074 kilometers 

e. 0.010 kilograms 

f. 300. grams 

g. 42 students 

Using significant digits in calculations 

Taking measurements and recording data are often a part of science classes. When you use the data in 

calculations, keep in mind this important principle: 

When using data in a calculation, your answer can’t be more precise than the least precise measurement. 

You are using a ruler to measure the length of each side of a rectangle.The 

ruler is marked in tenths of a centimeter. This means that you can estimate the 

distance between two 0.1 cm marks and make measurements that are to two 

places after the decimal. 

You measure the two short sides of the triangle and find that they each have a 

length of 12.25 cm. The long sides each have a length of 20.75 cm. 

The rectangle’s perimeter (distance around) is 12.25 cm + 20.75 cm + 12.25 cm + 20.75 cm, or 66.00 cm. The 

two zeros to the right of the decimal point show that you measured with a precision of 0.01 cm. 

The area of the rectangle is found by multiplying the length of the short side by the length of the long side. 

2 

12.25 cm× 20.75 cm = 

254.1875 cm 

The answer you get from you calculator has seven significant digits. This incorrectly implies that your ruler can 

measure to one ten-thousandth of a centimeter. Your ruler can’t measure distances that small! 

1.3

Page 3 of 4 

Follow these steps for determining the right answer for your calculation: 

• When multiplying or dividing measurements, find the measurement in the calculation with the least 

number of significant digits. After doing your calculation, round the answer to that number of 

significant digits. 

In the rectangle example on the previous page, each measurement has 4 significant digits. When you 

1.3 

multiply the measurements to find the area, your answer should be rounded to four significant digits. The 

area should be reported as 254.2 cm2 . 

• When adding or subtracting measurements, the answer must not contain more decimal places than your least 

accurate measurement. 

In the rectangle example, the perimeter is reported to two decimal places to show that your ruler measures 

length to the nearest 0.01 centimeter. 

It is important to note that when adding or subtracting, you are not concerned with the number of significant 

digits to the left of the decimal point. When adding 1.25 cm + 1,000.50 cm + 2,000,000.75 cm, the answer is 

2,001,002.50 cm. It is okay to have an answer with nine significant digits, because only TWO of them are to 

the right of the decimal point. 

• When you are finding the average of several measurements, remember that numbers found by counting have 

an infinite number of significant digits. 

For example, a student measures the distance between two magnets when their attractive force is first felt. 

He repeats the experiment three times. His results are: 23.25 cm, 23.30 cm, 23.20 cm. 

To find the average distance, He adds the three times and divides the sum by three. “Three” is the number of 

times the experiment is repeated. 

23.25 cm + 23.30 cm + 23.20 cm 

= 

23.25 cm 

3 

In this equation, the number 3 is found by counting the number of times the experiment is repeated, not by 

measuring something. Therefore it is said to have an infinite number of significant digits. That’s why the 

answer has four significant digits, not just one. 

Report your answers with significant digits 

Have you ever participated in a road race? The following problems are all related to a road race event. Can you 

come up with some other problems that you might have to solve if you were running in or volunteering for a road 

race? 

1. The banner over the finish line of a running race is 400. centimeters long and 85 centimeters high. What is 

the area of the banner?

Page 4 of 4 

2. Heidi stops at three water stations during the running race. She drinks 0.25 liters of water at the first 

stop, 0.3 liters at the second stop, and 0.37 liters at the third stop. How much water does she 

consume throughout the race? 

3. The race officials want to set up portable bleachers near the finish line. Each set of bleachers is 4.50 meters 

long and 2.85 meters wide. How many square meters of open ground space do they need for each set? 

4. The race has been held annually for ten years. The high temperatures for the race dates (in degrees Celsius) 

are listed in the table below. What is the average high temperature for the race day based on the temperatures 

for the past ten years? Write your answer in the bottom row in the table. 

Table 2: Race Day Temperatures for Each Year 

Year Number of Race Race Day Temperature (°C) 

1 27.2 

2 18.3 

3 28.9 

4 22.2 

5 20.6 

6 25.5 

7 21.1 

8 23.9 

9 26.7 

10 27.8 

Average Temperature 

5. Challenge! Ji-Sun has participated in the race for the past four years. His times, reported in 

minutes:seconds, were 

40:30 

43:40 

39:06 

38:52 

What is his average time to complete the race? (Hint: Convert all times to seconds before averaging!) 

6. Come up with one more problem that uses information that is related to a road race. Write your problem in 

the space below and come up with the answer. Be sure to write your answer with the correct number of 

significant digits. 

1.3

Name: Date: 

1.3 Study Notes 

This skill builder will help you take notes while you read. Each paragraph in the text has a sidenote. Fill in the 

table as you read each section of your textbook. Use the information to study for tests! 

• First, write in the number of the section that you are reading. For example, the first section of the text is 1.1. 

This is the first section in chapter 1 of the text. 

• For each paragraph that you read, write the sidenote. Then write a question based on this sidenote. As you 

read the paragraph, answer your own question! 

• When you study, fold this paper so that the answers are hidden. Use separate paper to write answers to each 

of your questions. Then unfold this paper and check your work. 

Section number: 1.1 

Page 

number 

Section number: __________ 

Sidenote text Question based on 

sidenote 

8 Accuracy What is the science 

definition of accuracy? 

Page 

number 


sidenote 

Answer to question 

1.3 

In science, accuracy means 

how close a measurement is 

to an accepted or true value. 

Answer to question

Page 2 of 2 

Section number: _________ 

Page 

number 


sidenote 

Answer to question 

1.3

Name: Date: 

1.3 Science Vocabulary 

One stumbling block for many science students is the number of new vocabulary words they encounter. Each 

field of science has its own body of terms, and there are many additional terms that are used in all the fields of 

science. However, few people are likely to run across these terms in their daily lives until they enter science 

classes in school. How do students master this new language? The same way they master any vocabulary— by 

looking to the roots! 

Prefixes and suffixes play an important role in word structure. Prefixes are word parts that begin a word, and 

suffixes are word parts that end a word. These parts, also called roots, often have special meanings due to their 

use in other languages. 

Prefixes and suffixes of words (and entire words themselves) in the English language are derived from other 

languages. Some of these languages like French are used in the world culture today and some languages belong 

to cultures long past. Latin and Greek are the two most common languages from which we derive pieces and 

parts of our words. 

The study of languages provides tremendous benefit to understanding the meanings of words. Other languages 

provide us with greater understanding of our own language since the roots of many of the words come from these 

languages. For example, English, French, Italian, and Spanish all have Latin as a common ancestral language. 

Therefore, studying French, Italian, or Spanish increases the size of your vocabulary toolbox. Studying Latin (or 

Greek) is also a tremendous aid for mastery and comprehension of the English vocabulary. 

When you encounter a new word and are unsure of its meaning, find and isolate the prefix and suffix of the word. 

It may help to write the word on a separate sheet of paper and circle or underline these parts. The remaining, 

uncircled parts of the word may also have a special meaning. Now, study each part of the word and work towards 

understanding its meaning. 

Consider the word blueberry. There are two pieces to this word—the prefix blue and the suffix berry. Each of 

these word parts has its own meaning which, when combined with the other word part, gives the whole word its 

own, unique meaning. Blue denotes a color with which you are familiar. A berry is a small fruit that birds (and 

humans!) like to eat. Put them together, and you understand that blueberry probably means a small fruit that is 

colored blue. From your past experiences, you realize that this is a pretty good description of blueberries. Science 

words can be broken apart and analyzed in the same way to get an understanding of their meanings. 

Below are some words you may encounter in a science class. For each word, circle the prefix and put a box 

around the suffix: 

thermometer electrolyte monoatomic 

volumetric endothermic spectroscope 

prototype convex supersaturated 

1.3

Page 2 of 3 

The table below lists some prefixes and suffixes that are found in scientific vocabulary along with their 

respective meanings. Use this table to write a definition for the following terms. 

Prefixes Suffixes 

homo – same, equal -escence – to exist 

poly – many -meter – measure 

hydro – water -ology – the study of 

lumen – light -mer – unit 

spectro – a continuous range or 

full extent 

hetero – different 

-geneous – kind or type 

1. hydrology _____________________________________ 

2. polymer _____________________________________ 

3. homogeneous _____________________________________ 

4. heterogeneous _____________________________________ 

5. luminescence _____________________________________ 

6. spectrometer _____________________________________ 

Now, using a dictionary, look up the words for which you provided your own definition, and write the formal 

definitions in the spaces below: 

1. hydrology _____________________________________ 

2. polymer _____________________________________ 

3. homogeneous _____________________________________ 

4. heterogeneous _____________________________________ 

5. luminescence _____________________________________ 

6. spectrometer _____________________________________ 

1.3

Page 3 of 3 

Using the table of prefixes and suffixes provided below, write a word that corresponds to each of the 

following definitions: 

Prefixes Suffixes 

thermo – heat -scope – to view 

mono – one -meter – measure 

tele – far -atomic – indivisible unit 

sono – sound, tone -graph, -gram – something written 

1. A device to measure heat or temperature: _____________________________________ 

2. A graph showing the loudness and frequencies of sounds: ________________________________ 

3. Having only one type of “indivisible” unit: _________________________________ 

4. A device used to view distant objects: _____________________________________ 

Look up the words you created in the dictionary. Write your words and the accepted definitions in the space 

below: 

Word Dictionary Definition 

How closely did your definitions match the accepted ones found in the dictionary? Your definitions based on 

your understanding of the roots for the prefixes and suffixes likely provided you with good results. A thorough 

knowledge of prefixes and suffixes will be a tremendous help to you as you proceed through your science 

education and will enable you to better understand the written and spoken language you encounter in your daily 

life. 

1.3

Name: Date: 

1.3 SI Unit Conversion—Extra Practice 

Science is about exploring and understanding the universe, from the tiniest subatomic particles to the mindboggling 

expanses of interstellar space. We gain understanding by asking questions, observing, measuring, and 

sharing results with others. You will use SI (metric) measuring tools for this purpose throughout the year. This 

skill sheet will help you become familiar with the SI prefixes you will use to measure length, mass, and volume. 

Here are the prefixes you will use to report measurements: 

Prefix kilo- hecto- deka- Basic unit 

(no prefix) 

1. How many centimeters are there in 24 meters? 

a. Restate the question: 24 meters = __________centimeters. 

b. Use the place value chart above to determine the 

multiplication factor, and solve. 

Count the number of places on the chart it takes to move 

from meters (the ones place) to centimeters (the 

hundredths place). Since it takes 2 moves to the right, 

the multiplication factor is 100. Move the decimal two places to the right. 

Solution: multiply 24 × 100 = 2,400. 

Answer: There are 2,400 centimeters in 24 meters. 

Use the chart above to help you answer the following questions. 

Part A: Distance conversions 

1. Earth’s diameter is 12,756 kilometers. How many meters is this? 

2. The diameter of Earth’s moon is 3,476 kilometers. Express this distance in centimeters. 

deci- centi- milli- 

Symbol k h da m, g, l d c m 

Multiplication Factor 

or Place-Value 

1,000 100 10 1 0.1 0.01 0.001 

3. The average distance between Earth and its moon is 384,000,000 meters. Express this distance in kilometers. 

4. A billion years ago, Earth and its moon were just 200,000 kilometers apart. Express this distance in meters. 

1.3

Page 2 of 2 

5. Earth’s moon is covered with impact craters. These craters form when an asteroid, comet, or 

meteorite crashes into the moon’s surface. The largest impact crater, called Clavius, is 160 

kilometers across. How many centimeters is this? 

6. A crater known as Aristarchus is 3.6 kilometers deep. What is this distance in millimeters? 

7. Another feature of the moon’s surface is long, narrow valleys called Rilles. The Hadley Rille is 

125 kilometers long, 0.4 kilometers deep, and 1.5 kilometers wide at its widest point. Express these 

distances in meters. 

8. To escape Earth’s gravitational pull, an object must reach a speed of 11,180 meters per second. How fast is 

this in kilometers per second? 

Part B: Mass conversions 

9. The largest land mammal is the African Elephant. The average adult has a mass of 5,400 kilograms. Express 

this mass in grams. 

10. One of the smallest mammals is the bumblebee bat, with a mass of about 0.002 kilograms. Express this mass 

in grams. 

11. A pygmy shrew is another tiny mammal, with a mass ranging from 1.2 grams to 2.7 grams. Express these 

measurements in milligrams. 

12. The largest mammal ever found on Earth was a female blue whale with a mass of more than 

158,000,000 grams. Express this mass in kilograms. 

13. A blue whale’s heart is so large that a person could crawl through its largest blood vessel (the aorta). The 

heart has a mass of about 450 kg. Express this mass in milligrams. 

14. A baby blue whale will drink between 23 and 90 kilograms of milk each day. Express these masses in grams. 

Part C: Volume conversions 

15. A mature sugar maple tree produces about 40 liters of sap each season. How many milliliters is this? 

16. After the sap is collected, extra water in it must be boiled off. Forty liters of sap is boiled down to produce 

one liter of maple syrup. How many milliliters of syrup are in one liter? 

17. Canada is the world’s largest commercial producer of maple syrup. In 2005, Canada produced about 

26,600,000 liters of maple syrup. How many kiloliters is this? 

18. Vermont is the United States’ largest commercial producer of maple syrup. Vermont produced about 

1,558 kiloliters of maple syrup in 2005. How many liters is this? 

19. One serving of maple syrup is 1/4 cup, or 0.06 liters. How many milliliters of syrup is this? 

20. A jug of maple syrup contains 947 milliliters. Express this volume in liters. 

1.3

Name: Date: 

1.3 SI-English Conversions 

Even though the United States adopted the SI system in the 1800’s, most Americans still use the English system 

(feet, pounds, gallons, etc.) in their daily lives. Because almost all other countries in the world, and many 

professions (medicine, science, photography, and auto mechanics among them) use the SI system, it is often 

necessary to convert between the two systems. 

It is useful to be familiar with examples of measurements in both systems. Most people in the United States are 

very familiar with English system units because they are used in everyday tasks. Some examples of SI system 

measurements are: 

One kilometer (1 km) is about two and a half 

times around a standard running track. 

One centimeter (1 cm) is about the width of 

your little finger. 

One kilogram (1 kg) is about the mass of a full 

one-liter bottle of drinking water. 

One gram (1 g) is about the mass of a paper 

clip. 

One liter (1 l) is a common size of a bottle of 

drinking water. 

One milliliter (1 mL) is about one droplet of 

liquid. 

1.3

Page 2 of 3 

When precise conversions between SI and English systems are necessary, you will need to know the 

conversion factors given in the table below. 

Table 1: English - SI measurement equivalents 

Measurement Equivalents 

Length: 1 inch = 2.54 centimeters 

Volume: 

Mass: Weight 

(on Earth) 

1. If we need to know the mass of a 50.-pound bag of dog food in kilograms, we take the following steps: 

(1) Restate the question: 50. lb ≈ __________ kg 

(2) Find the conversion factor from the table: 1 kg ≈ 2.2 lb 

(3) Multiply the ratios making sure that the unwanted units cancel, leaving only the desired units (kilograms) 

in the answer: 

2. How many inches are equivalent to 99 centimeters? 

1kilometer ≈ 0.62 mile 

1 liter ≈ 1.06 quart 

1 kilogram ≈ 2.2 pounds 

1 ounce ≈ 28 grams 

50 

----------lb 

------------- 

1 kg 50 kg 

• ≈ ------------- ≈22.7272 kg ≈23 

kg 

1 2.2 lb 2.2 

(1) Restate the question: 99 centimeters = __________ inches 

(2) Find the conversion factor from the table: 1 inch = 2.54 centimeters. 

(3) Multiply the ratios. Make sure the units cancel correctly to produce the desired unit in the answer. 

99 cm 1 in 

-------------- • ------------------ 

1 2.54 cm 

99 in 

= ----------- = 38.97638 in ≈ 39 inches 

2.54 

3. An eighth grader is 5 feet 10. inches tall. We want to know how many centimeters that is without measuring. 

(1) Restate the question: 5 feet 10. inches = __________ centimeters 

(2) Convert units within one system if necessary: 5 feet 10. inches needs to be rewritten as either feet or 

inches. Since our conversion factor (from the table) is given as 1 inch = 2.54 centimeters, it makes sense to 

rewrite the quantity 5 feet 10. inches as some number of inches. First convert the number of feet (5) to 

inches, then add 10. inches. Since there are 12 inches in 1 foot, use that as your conversion factor to 

calculate: 

5 

------ft 

12 in 

• ----------- 

1 1 ft 

60 in · 

= ----------- = 

60 inches 

1 

1.3

Page 3 of 3 

1. 

2. 

3. 

Now add: 60. inches + 10. inches = 70. inches. 5 feet 10. inches = 70. inches. We now need to 1.3 

convert 70. inches to centimeters. 

(3) Restate the question: 70. inches = __________ centimeters. 

(4) Choose the correct conversion factor from the table. Here, we want to convert inches to centimeters, so 

use 1 inch = 2.54 centimeters. 

(5) Multiply the ratios. Make sure the units cancel correctly to produce the desired type of unit in the answer. 

7.0 km ≈ __________ mi 

115 g ≈ __________oz 

2,000. lb. ≈ 

__________kg 

70 

----------in 

2.54 cm 

• ------------------ 

1 1 in 

4. A 2.0-liter bottle of soda is about how many quarts? 

= 

177.8 

--------------------cm 

= 180 cm 

1 

5. A pumpkin weighs 5.4 pounds. What is its mass in grams? (Hint: There are 16 ounces in one pound). 

6. Felipe biked 54 kilometers on Sunday. How many miles is this? 

7. How many inches are in 72.0 meters? How many yards is this? 

8. In a track meet, Julian runs the 800. meter dash, the 1600. meter run, and the opening leg of the 

4 × 400. meter relay. How many miles is this altogether? 

9. How many liters are equivalent to 1.0 gallon? (There are exactly four quarts in a gallon.) 

10. The mass of a large order of french fries is about 170. grams. What is its approximate weight in pounds?

Name: Date: 

1.4 Creating Scatterplots 

Scatterplots allow you to present data in a form that shows a cause and effect relationship between two variables. 

The parts of a scatterplot include: 

1. Data pairs: Scatterplots are made using pairs of numbers. Each pair of numbers represents one data point on 

a graph. The first number in the pair represents the independent variable and is plotted on the x-axis. The 

second number represents the dependent variable and is plotted on the y-axis. 

2. Axis labels: The label on the x-axis is the name of the independent variable. The label on the y-axis is the 

name of the dependent variable. Be sure to write the units of each variable in parentheses after its label. 

3. Scale: The scale is the quantity represented per line on the graph. The scale of the graph depends on the 

number of lines available on your graph paper and the range of the data. Divide the range by the number of 

lines. To make the calculated scale easy-to-use, round the value to a whole number. 

4. Title: The format for the title of a graph is: “Dependent variable name versus independent variable name.” 

1. For each data pair in the table, identify the independent and dependent variable. Then, rewrite the data pair 

according to the headings in the next two columns of the table The first two data pairs are done for you. 

Data pair 

(not necessarily in order) 

Independent 

(x-axis) 

Dependent 

(y-axis) 

1 Temperature Hours of heating Hours of heating Temperature 

2 Stopping distance Speed of a car Speed of a car Stopping distance 

3 Number of people in a family Cost per week for groceries 

4 Stream flow rate Amount of rainfall 

5 Tree age Average tree height 

6 Test score Number of hours studying for a test 

7 Population of a city Number of schools needed 

2. Using the variable range and number of lines, calculate the scale for an axis. The first two are done for you. 

Variable 

range 

Number of lines Range ≥ Number of lines Calculated scale Adjusted scale 

13 24 13 ≥ 24 = 0.54 1 

83 43 83 ≥ 43 = 1.9 2 

31 35 

100 33 

300 20 

900 15 

1.4

Page 2 of 3 

3. Here is a data set to use to create a scatterplot. Follow these steps to make the graph. 

a. Place this data set in the table below. Each data point is given in the format of (x, y). 

The x- values represent time in minutes. The y-values represent distance in kilometers. 

(0, 5.0), (10, 9.5), (20, 14.0), (30, 18.5), (40, 23.0), (50, 27.5), (60, 32.0). 

Independent variable 

(x-axis) 

Dependent variable 

(y-axis) 

b. What is the range for the independent variable? 

c. What is the range for the dependent variable? 

d. Make your graph using the blank graph below. Each axis has twenty lines (boxes). Use this information 

to determine the adjusted scale for the x-axis and the y-axis. 

e. Label your scatterplot. Add a label for the x-axis, y-axis, and provide a title. 

f. Draw a smooth line through the data points. 

1.4

Page 3 of 3 

g. What is the position value after 45 minutes? Use your scatterplot to answer this question. 

1.4

Name: Date: 

1.4 What’s the Scale? 

Graphs allow you to present data in a form that is easy to understand. With a graph, you can see whether your 

data shows a pattern and you can picture the relationship between your variables. 

The scale on a graph is the quantity represented per line on the graph. Your graph’s scales will depend on the type 

of data you are plotting. Each of your graph’s axes has its own separate scale. You need to be consistent with your 

scales. If one line on a graph represents 1 cm on the x-axis, it has to stay that way for the entire x-axis. 

When figuring out the scale for your graph, you first need to know the range. When you want your axis to start at 

zero, your range is equal to your highest data value. Once you have the range, you can calculate the scale. Count 

the number of lines you have available on your graph paper. Now, divide the range by the number of lines. This 

number is your scale. Then you adjust your scale by rounding up to a whole number. 

Calculate the scales for the data set listed in the table below. Your graph paper is 20 boxes by 20 boxes. 

Identify the variables. 

1. Which is the independent variable? Time is your independent variable; it goes on the x-axis. 

Which is the dependent variable? Amount of rainfall is your dependent variable; it goes on the y-axis. 

Find the ranges. 

2. What is the range of data for the x-axis? 30 hours 

What is the range of data for the y-axis? 59 mL 

Calculate the scales. 

Time (hours) Amount of rainfall (mL) 

5 5 

10 11 

15 21 

20 28 

25 37 

30 59 

3. What is the scale for your x-axis? 

30 hrs divided by 20 boxes = 1.5 hrs/box rounded up to 2 hrs/box 

Each line on the graph is equal to 2 hours. 

The x-axis will start at zero and go up to 40 hours, with each line counting as 2 hours. 

What is the scale for your y-axis? 

59 mL divided by 20 boxes = 2.95 mL/box rounded up to 3 mL/box 

Each line on the graph is equal to 3 mL. 

The y-axis will start at zero and go up to 60 mL, with each line counting as 3 mL. 

1.4

Page 2 of 2 

1.4 

1. Given the variable range and the number of lines, calculate the scale for an axis. Often the 

calculated scale is not an easy-to-use value. To make the calculated scale easy-to-use, round the value and 

write this number in the column with the heading “Adjusted scale.” The first two are done for you. 

Range 

from 0 

Number 

of Lines 

Range ≥ Number of Lines Calculated scale Adjusted scale 

(whole number) 

14 10 14 ≥ 10 = ≥ 1.4 2 

8 5 8 ≥ 5 =≥ 1.6 2 

1000 20 1000 ≥ 20 = ≥ 

547 15 547 ≥ 15 = ≥ 

99 30 99 ≥ 30 = ≥ 

35 12 35 ≥ 12 = ≥ 

2. Calculate the range and the scale for the x-axis starting at zero, given the following data pairs and a 30 box 

by 30 box piece of graph paper. Each data point is given in the format of (x, y): (1, 27), (30, 32), (20, 19), 

(6, 80), (15, 21). 

3. Calculate the range and the scale for the y-axis starting at zero, given the following data pairs and a 10 box 

by 10 box piece of graph paper. Each data point is given in the format of (x, y): (1, 5), (2, 10), (3, 15), (4, 20), 

(5, 25). 

4. Calculate the scale for both the x-axis and the y-axis of a graph using the data set in the table below. Your 

graph paper is 20 boxes by 20 boxes. Start both the x- and y-axis at zero. 

a. Which is the independent variable? Which is the dependent variable? 

b. What is the range of data for the x-axis? What is the range of data for the y-axis? 

c. What is the scale for your x-axis? What is the scale for your y-axis? 

Day Average Daily 

Temperature (°F) 

1 67 

3 68 

5 73 

7 66 

9 70 

11 64

Name: Date: 

1.4 Interpreting Graphs 

The four main kinds of graphs are scatterplots, bar graphs, pie graphs, and line graphs. 

To learn how to interpret graphs, we will start with an example of a scatterplot. The data presented on the 

scatterplot below is the amount of money in a cash box during a car wash that lasted for five hours. Use this 

graph to follow the steps and answer the questions below. 

Step 1: Read the labels on the graph. 

1. What is the title of the graph? 

2. Read the labels for the x-axis and the y-axis. What two variables are represented on the graph? 

Step 2: Read the units used for the variable on the x-axis and the variable 

on the y-axis. 

3. What unit is used for the variable on the x-axis? 

4. What unit is used for the variable on the y-axis? 

1.4

Page 2 of 3 

Step 3: Look at the range of values on the x- and y-axes. Do the range of values make 

sense? What would the data look like if the range of values on the axes was 

spread out more or less? 

5. What is the range of values for the x-axis? 

6. The range of values for the y-axis is 0 to $120. What would the graph look like if the range of values was 

0 to $500? Where would the data appear on the graph if this were the case? 

Step 4: After looking at the parts of the graph, pay attention to the data that is plotted. Is there 

a relationship between the two variables? 

7. Is there a relationship between the variables that are represented on the graph? 

Step 5: Write a sentence that describes the information presented on the graph. For example, 

you may say, “As the values for the variable on the x-axis increase, the values for the 

variable on the y-axis decrease.” 

8. Write your own description of the graph. 

9. The theater club at your school needs to raise $1000 for a trip that they want to take. They will be taking the 

trip next fall. It is now April. Based on the graph, would you recommend that the group wash cars to raise 

money? Write out a detailed response to this question. Be sure to provide evidence to support your reasons 

for your recommendation. 

Now, apply what you know about interpreting graphs to a 

bar graph. Use the steps from part one to help you answer 

the questions. 

1. What is the title of this graph? 

2. What variables are represented on the graph? (Hint: there 

are three variables.) Describe each variable in terms of the 

categories or the range of values used. 

3. Write a sentence that describes how the percentage of 

teenagers employed compares from city to city. Do not 

state any conclusions about the data in your sentence. 

4. Write a sentence that describes how the percentage of boys 

employed compares to the percentage of girls employed. 

Do not state any conclusions about the data in your 

sentence. 

5. Based on the data represented in the graph, come up with a hypothesis for why the percentage of teenagers 

employed differs from city to city. 

6. Based on the data represented in the graph, come up with a hypothesis to explain the employment 

differences between boys and girls in these cities. 

1.4

Page 3 of 3 

Now, apply what you know about interpreting 

graphs to a pie graph. Use the steps from part one 

to help you answer the questions. 


2. What variables are represented on the graph? 

(Hint: there are two variables.) 

3. Are any units used in this graph? Explain your 

answer. 

4. If you were going to report on this data, what 

would you say? Write two to three sentences that 

describe this graph. Do not state any conclusions 

about the data in your sentence. 

5. Come up with a hypothesis based on the data in 

this graph. Briefly describe how you would test your hypothesis. 

6. Do you have a job? If so, in which category does your job fit? Do you think this pie graph accurately 

represents the working teenager population in your area? Explain your response. 

Finally, apply what you know about interpreting graphs to a 

line graph. Use the steps from part one to help you answer 

the questions. 


2. What variables are represented on the graph? (Hint: there 

are two variables.) 

3. What is the range of values for each variable? 

4. Write a sentence that describes the change in student 

population at Springfield High School from 1970 to 1985. 

Do not state any conclusions about the data in your 

sentence. 

5. a. Come up with a possible reason for the sudden drop in 

population between 1980 and 1985. 

b. If this were your high school, how could you find out if your explanation is correct? 

6. Explain why this graph is a line graph, not a scatterplot. 

1.4

Name: Date: 

1.4 Recognizing Patterns on Graphs 

In physical science class, you will do laboratory experiments to answer questions such as: If I change this, what 

will happen to that? For example, you might ask: If I change the mass of a toy car by adding some cargo, what 

will happen to its acceleration down a ramp? Or, you might ask: If I change the temperature of some water in a 

beaker by heating it on a burner, what will happen to the amount of sugar that I can dissolve in it? 

Making a scatterplot graph of your results can help you recognize patterns in your data. In order to share your 

results with others, it is helpful to understand the vocabulary that scientists use to describe patterns seen on 

scatterplot graphs. In this skill sheet, you will practice describing some of these patterns. 

Take a look at these two graphs: 

In each case, the line or curve slopes up from left to right. This tells you there is a direct relationship between 

the x- and y-variables. If you increase the x-value, the y-value will also increase. 

Here are two more graphs: 

Direct relationship between variables 

Inverse relationship between variables 

1.4

Page 2 of 3 

In each case, the line or curve slopes down from left to right. This tells you there is an inverse 

relationship between the x- and y-variables. If you increase the x-value, the y-value will decrease. 

Sometimes your graphs will be a straight line. This tells you there is a linear relationship between 

variables. 

If the graph is a curve, we say that the relationship is non-linear. 

Scatterplots can also help us describe the strength of the relationship between two variables. The following 

graphs show the number of grams of three different substances that will dissolve in 100 ml of water at different 

temperatures. 

No relationship Weak relationship Strong relationship 

Substance A: The amount that will dissolve is not related to temperature. No relationship. 

Substance B: The amount that will dissolve increases slightly with temperature. This is a weak relationship. 

Substance C: The amount that will dissolve increases a lot with temperature. This is a strong relationship. 

1.4

Page 3 of 3 

Answer the following questions about graphs A–F, below. 

1. Name three graphs which show a direct relationship between variables. 

2. Name two graphs which show an inverse relationship between variables. 

3. Name three graphs which show a linear relationship between variables. 

4. Name two graphs which show non-linear relationships. 

5. In which graph does a change in the x-variable cause NO CHANGE in the y-variable? 

6. Which graph shows a stronger relationship between variables, graph A or graph F? 

1.4

Name: Date: 

2.1 Scientific Processes 

The scientific method is a process that helps you find answers to your questions about the world. The process 

starts with a question and your answer to the question based on experience and knowledge. This “answer” is 

called your hypothesis. The next step in the process is to test your hypothesis by creating experiments that can be 

repeated by other people in other places. If your experiment is repeated many times with the same results and 

conclusions, these findings become part of the body of scientific knowledge we have about the world. 

1. Ask a question. 

2. Formulate a hypothesis. 

Read the following story. You will use this story to practice using the scientific method. 

Maria and Elena are supposed to help their mom chill some soda by putting the cans into a bucket filled with 

ice cubes, but Maria forgot to fill the ice cube trays. Elena says that she remembers reading somewhere that 

hot water freezes faster than cold water. Maria is skeptical. She learned in science class that the hotter the 

liquid, the faster the molecules are moving. Since hot water molecules have to slow down more than cold 

water molecules to become ice, Maria thinks that it will take hot water longer to freeze than cold water. 

The girls decide to conduct a scientific experiment to determine whether it is faster to make ice cubes with 

hot water or cold water. 

Now, answer the following questions about the process they used to reach their conclusion. 

Asking a question 

1. What is the question that Maria and Elena want to answer by performing an experiment? 

Formulate a hypothesis 

2. What is Maria’s hypothesis for the experiment? State why Maria thinks this is a good hypothesis. 

Design and conduct an experiment 

Steps to the Scientific Method 

3. Design an experiment to test your hypothesis. 

4. Conduct an experiment to test your hypothesis and collect the data. 

5. Analyze data. 

6. Make a tentative conclusion. 

7. Test your conclusion, or refine the question, and go through each step again. 

3. Variables: There are many variables that Maria and Elena must control so that their results will be valid. 

Name at least four of these variables. 

2.1

Page 2 of 2 

4. Measurements: List at least two types of measurements that Maria and Elena must make during 

their experiment. 

5. Procedure: If Maria and Elena want their friends to believe the results of their experiment, they 

need to conduct the experiment so that others could repeat it. Write a procedure that the girls could follow to 

answer their question. 

Collect and analyze data 

The girls conducted a carefully controlled experiment and found that after 3 hours and 15 minutes, the hot water 

had frozen solid, while the trays filled with cold water still contained a mixture of ice and water. They repeated 

the experiment two more times. Each time the hot water froze first. The second time they found that the the hot 

water froze in 3 hours and 30 minutes. The third time, the hot water froze in 3 hours and 0 minutes. 

6. What is the average time that it took for hot water in ice cube trays to freeze? 

7. Why is it a good idea to repeat your experiments? 

Make a tentative conclusion 

8. Which of the following statements is a valid conclusion to this experiment? Explain your reasoning for 

choosing a certain statement. 

a. Hot water molecules don’t move faster than cold water molecules. 

b. Hot water often contains more dissolved minerals than cold water, so dissolved minerals must help 

water freeze faster. 

c. Cold water can hold more dissolved oxygen than hot water, so dissolved oxygen must slow down the 

rate at which water freezes. 

d. The temperature of water affects the rate at which it freezes. 

e. The faster the water molecules are moving, the faster they can arrange themselves into the nice, neat 

patterns that are found in solid ice cubes. 

Test your conclusion or refine your question 

Maria and Elena are pleased with their experiment. They ask their teacher if they can share their findings with 

their science class. The teacher says that they can present their findings as long as they are sure their conclusion 

is correct. 

The last step of the scientific method is important. At the end of any set of experiments and before you present 

your findings, you want to make sure that you are confident about your work. 

9. Let’s say that there is a small chance that the results of the experiment that Maria and Elena performed were 

affected by the kind of freezer they used in the experiment. What could the girls do to make sure that their 

results were not affected by the kind of freezer they used? 

10. Statement 8(b) suggests a possible reason why temperature affects the speed at which water freezes. Refine 

your original question for this experiment. In other words, create a question for an experiment that would 

prove or disprove statement 8(b). 

2.1

Name: Date: 

2.1 What’s Your Hypothesis? 

After making observations, a scientist forms a question based on observations and then attempts to answer that 

question. A guess or a possible answer to a scientific question based on observations is called a hypothesis. It is 

important to remember that a hypothesis is not always correct. A hypothesis must be testable so that you can 

determine whether or not it is correct. 

In science class your teacher has told you that the ability of a river to transport material depends on how fast the 

river is flowing. Imagine the river has three speeds—slow, medium, and fast. Now, imagine the river bottom has 

sand, marble-sized pebbles, and baseball-sized rocks. Come up with a hypothesis for the answer to the following 

question. Then, justify your reasoning: 

Research question: At which flow rate—slow, medium, or fast—would a river be able to transport baseballsized 

rock? 

Example hypothesis and justification: The river would have to be flowing at a fast flow rate to be able to 

transport baseball-sized rocks. It takes more force to move larger rocks than small pebbles and sand. Fast flowing 

water has more pushing force than medium or slow flowing water. I know this from an experience I had wading 

in a river one time. As I waded from still water to areas where the river was flowing faster, I could feel the water 

pushing against my legs more and more. 

1. You left a glass full of water by a window in your house in the morning. Three hours later you walk by the 

glass, and the water level is noticeably lower than it was in the morning. You have made the observation that 

the water level in the cup is lower. Then, you ask the following question: “Why is the water level in the cup 

lower?” 

What is a possible hypothesis you could make? 

2.1

Page 2 of 2 

2. Your teacher shows you a demonstration in which there is a box with two chimneys. Under one 

chimney is a lit candle, and under the other chimney is smoke from burning incense. You observe 

2.1 

that the smoke always goes towards the candle and then exits the box from the chimney above the 

candle. You ask the following question: “Why does the smoke go toward the candle and leave the chimney 

above the candle?” 


3. You have learned in science class that evaporation is a process that describes when a liquid turns to a gas at 

a temperature below the boiling point. You are now about to investigate evaporation and factors that may 

increase the rate at which it occurs. You ask the question, “What causes the evaporation rate of water to 

increase?” 


4. Rivers and streams flow at various speeds. You ask, “What factors increase the flow rate of a river?” 


5. It is late fall and you notice that flower bulbs in your yard have been dug up and some have been eaten. You 

ask, “What has happened?” 


6. You know that sea otters eat sea urchins and that sea urchins eat kelp. You ask, “What would happen to this 

ecosystem if all the kelp died?” 


7. In Alaska, lynx (wild cats) are predators of the snowshoe hare. In the wintertime, the coat of the snowshoe 

hare turns from brown to white. You ask, “Why does the snoeshoe hare change color in the winter?” 


8. In the deserts of the southwestern United States, coyotes are dog-like animals that eat many different things 

such as small animals and cactus fruit. They are also scavengers, which means they eat dead and decaying 

animals. You ask, “Are there coyote-like animals that serve as predator-scavengers in other deserts on other 

continents?” 

What is a possible hypothesis you could make?

Name: Date: 

2.2 Recording Observations in the Lab 

How do you record valid observations for an experiment in the lab? 

When you perform an experiment you will be 

making important observations. You and others 

will use these observations to test a hypothesis. 

In order for an experiment to be valid, the 

evidence you collect must be objective and 

repeatable. This investigation will give you 

practice making and recording good 

observations. 

Making valid observations 

Valid scientific observations are objective and repeatable. Scientific observations are limited to one's senses and 

the equipment used to make these observations. An objective observation means that the observer describes only 

what happened. The observer uses data, words, and pictures to describe the observations as exactly as possible. 

An experiment is repeatable if other scientists can see or repeat the same result. The following exercise gives you 

practice identifying good scientific observations. 

Exercise 1 

Materials 

• Paper 

• Pencil 


• Ruler 

1. Which observation is the most objective? Circle the correct letter. 

a. My frog died after 3 days in the aquarium. I miss him. 

b. The frog died after 3 days in the aquarium. We will test the temperature and water conditions to 

find out why. 

c. Frogs tend to die in captivity. Ours did after three days. 

2. Which observation is the most descriptive? Circle the correct letter. 

a. After weighing 3.000 grams of sodium bicarbonate into an Erlenmeyer flask, we slowly added 

50.0 milliliters of vinegar. The contents of the flask began to bubble. 

b. We weighed the powder into a glass container. We added acid. It bubbled a lot. 

c. We saw a fizzy reaction. 

3. Which experiment has enough detail to repeat? Circle the correct letter. 

a. Each student took a swab culture from his or her teeth. The swab was streaked onto nutrient agar 

plates and incubated at 37 C. 

b. Each student received a nutrient agar plate and a swab. Each student performed a swab culture of 

his or her teeth. The swab was streaked onto the agar plate. The plates were stored face down in 

the 37 C incubator and checked daily for growth. After 48 hours the plates were removed from the 

incubator and each student recorded his or her results. 

c. Each student received a nutrient agar plate and a swab. Each student performed a swab culture of 

his or her teeth. The swab was streaked onto the agar plate. The plates were stored face down in 

the 37 C incubator and checked daily for growth. After 48 hours the plates were removed from the 

incubator and each student counted the number of colonies present on the surface of the agar.

Page 2 of 4 

Recording valid observations 

As a part of your investigations you will be asked to record observations on a skill sheet or in the results 

section of a lab report. There are different ways to show your observations. Here are some examples: 

1. Short description: Use descriptive words to explain what you did or saw. Write complete sentences. Give as 

much detail as possible about the experiment. Try to answer the following questions: What? Where? When? 

Why? and How? 

2. Tables: Tables are a good way to display the data you have collected. Later, the data can be plotted on a 

graph. Be sure to include a title for the table, labels for the sets of data, and units for the values. Check values 

to make sure you have the correct number of significant figures. 

Year 

manufactured 

Mass 

(grams) 

U.S. penny mass by year 

1977 1978 1979 1980 1981 1982 1983 1984 1985 

3.0845 3.0921 3.0689 2.9915 3.0023 2.5188 2.5042 2.4883 2.5230 

3. Graphs and charts: A graph or chart is a picture of your data. There are different kinds of graphs and 

charts: line graphs, trend charts, bar graphs, and pie graphs, for example. A line graph is shown below. 

Label the important parts of your graph. Give your graph a title. The x-axis and y-axis should have labels for 

the data, the unit values, and the number range on the graph. 

The line graph in the example has a straight line through the data. Sometimes data does not fit a straight line. 

Often scientists will plot data first in a trend chart to see how the data looks. Check with your instructor if 

you are unsure how to display your data.

Page 3 of 4 

4. Drawings: Sometimes you will record observations by drawing a sketch of what you see. The 

example below was observed under a microscope. 

Give the name of the specimen. Draw enough detail to make the sketch look realistic. Use color, when 

possible. Identify parts of the object you were asked to observe. Provide the magnification or size of the 

image. 

Exercise 2: Practice recording valid observations 

A lab report form has been given to you by your instructor. This exercise gives you a chance to read through an 

experiment and fill in information in the appropriate sections of the lab report form. Use this opportunity to 

practice writing and graphing scientific observations. Then answer the following questions about the experiment. 

A student notices that when he presses several pennies in a pressed penny machine, his brand new penny has 

some copper color missing and he can see silver-like material underneath. He wonders, “Are some pennies made 

differently than others?” The student has a theory that not all U.S. pennies are made the same. He thinks that if 

pennies are made differently now he might be able to find out when the change occurred. He decides to collect a 

U.S. penny for each year from 1977 to the present, record the date, and take its mass. The student records the data 

in a table and creates a graph plotting U.S. penny mass vs. year. Below is a table of some of his data: 

Year 

manufactured 

Mass 

(grams) 

U.S. penny mass by year 

1977 1978 1979 1980 1981 1982 1983 1984 1985 

3.0845 3.0921 3.0689 2.9915 3.0023 2.5188 2.5042 2.4883 2.5230 


a. What observation did the student make first before he began his experiment?

Page 4 of 4 

b. How did the student display his observations? 

c. In what section of the lab report did you show observations? 

d. What method did you use to display the observations? Explain why you chose this one.

Name: Date: 

2.2 Writing a Lab Report 

How do you share the results of an experiment? 

A lab report is like a story about an experiment. The details in the story help others learn from what you 

did. A good lab report makes it possible for someone else to repeat your experiment. If their results and 

conclusions are similar to yours, you have support for your ideas. Through this process we come to 

understand more about how the world works. 

The parts of a lab report 

A lab report follows the steps of the scientific method. Use the checklist below to create your own lab reports: 

� Title: The title makes it easy for readers to quickly identify the topic of your experiment. 

� 

� 

Research question: The research question tells the reader exactly what you want to find out 

through your experiment. 

Introduction: This paragraph describes what you already know about the topic, and shows how this 

information relates to your experiment. 

� Hypothesis: The hypothesis states the prediction you plan to test in your experiment. 

� Materials: List all the materials you need to do the experiment. 

� 

� 

� 

� 

Procedure: Describe the steps involved in your experiment. Make sure that you provide enough 

detail so readers can repeat what you did. You may want to provide sketches of the lab setup. 

Be sure to name the experimental variable and tell which variables you controlled. 

Data/Observations: This is where you record what happened, using descriptive words, data tables, 

and graphs. 

Analysis: In this section, describe your data in words. Here’s a good way to start: My data shows 

that... 

Conclusion: This paragraph states whether your hypothesis was correct or incorrect. It may suggest 

a new research question or a new hypothesis. 

A sample lab report 

Use the sample lab report on the next two pages as a guide for writing your own lab reports. Remember that you 

are telling a story about something you did so that others can repeat your experiment.

Page 2 of 3 

Name: Lucy O. Date: January 24, 2007 

Title: Pressure and Speed 

Research question: How does pressure affect the speed of the CPO air rocket? 

Introduction: 

Air pressure is a term used to describe how tightly air molecules are packed into a certain space. When air 

pressure increases, more air molecules are packed into the same amount of space. These molecules are moving 

around and colliding with each other and the walls of the container. As the number of molecules in the container 

increases, the number of molecular collisions in the container increases. A pressure gauge measures the force of 

these molecules as they strike a surface. 

In this lab, I will measure the speed of the CPO air rocket when it is launched with different amounts of initial 

pressure inside the plastic bottle. I want to know if a greater amount of initial air pressure will cause the air rocket 

to travel at a greater speed. 

Hypothesis: When I increase the pressure of the air rocket, the speed will increase. 

Materials: 

CPO air rocket CPO photogates 

CPO timer Goggles 

Procedure: 

1. I put on goggles and made sure the area was clear. 

2. The air rocket is attached to an arm so that it travels in a circular path. 

After it travels about 330°, the air rocket hits a stopper and its flight ends. 

I set up the photogate at 90°. 

3. My control variables were the mass of the rocket and launch technique, so 

I kept these constant throughout the experiment. 

4. My experimental variable was the initial pressure applied to the rocket. I 

tested the air rocket at three different initial pressures. The pressures that 

work effectively with this equipment range from 15 psi to 90 psi. I tested 

the air rocket at 20 psi, 50 psi, and 80 psi. I did three trials at each pressure. 

5. The length of the rocket wing is 5 cm. The wing breaks the photogate’s light beam. The photogate reports the 

amount of time that the wing took to pass through the beam. Therefore, I used wing length as distance and 

divide by time to calculate speed of the air rocket. 

6. I found the average speed in centimeters per second for each pressure.

Page 3 of 3 

Data/Observations: 

Analysis: 

My graph shows that the plots of the data for photogates A and B are linear. As the values for pressure increased, 

the speed increased also. 

Conclusion: 

Air pressure and speed of rocket 

Initial air pressure Time (sec) at 90° Speed (m/sec) at 90° Average speed 

cm/sec 

0.0227 2.20 

20 psi 

0.0231 2.16 

216 

0.0237 2.11 

0.0097 5.15 

50 psi 

0.0099 5.05 

510 

0.0098 5.10 

0.0060 8.33 

80 psi 

0.0064 7.81 

794 

0.0065 7.69 

The data shows that pressure does have an effect on speed. The graph shows that my hypothesis is correct. As the 

initial pressure of the rocket increased, the speed of the rocket increased as well. There is a direct relationship 

between pressure and speed of the rocket.

Name: Date: 

2.2 Using Computer Spreadsheets 

Computer spreadsheets provide an easy way to organize and evaluate data that you collect from an experiment. 

Numbers are typed into boxes called “cells.” The cells are organized in rows and columns. You can find the 

average of a lot of numbers or do more complicated calculations by writing formulas into the cells. Each cell has 

a name based on its column letter and row number. For example, the first cell in most spreadsheets is “A1.” 

This skill sheet will show you how to: 

1. Record data in a computer spreadsheet program. 

2. Do simple calculations for many data values at once using the 

spreadsheet. 

3. Make a graph with the data set. 

To complete this skill sheet, you will need: 

• Simple calculator 

• Access to a computer with a spreadsheet program 

1. Adding data: Open the spreadsheet program on your computer. You will see a window open that has rows 

and columns. The rows are numbered. The columns are identified by a letter. 

a. As shown in the graphic above, add headings for columns A, B, and C: 

cell A1, type “Time (sec)” 

cell B1, type “Temp (deg C)” 

cell C1, type “Slope” 

NOTE: You can change the width of the columns on your spreadsheet by clicking on the right-hand 

border and dragging the border to the left or right. 

b. Highlight column B. Then, go to the Format menu item and click on Cells. Make the format of these 

cells Number with one decimal place. Highlight column C and make the format of these cells Number 

with two decimal places. 

c. Type in the data for Time and Temperature as shown in the graphic above. 

2. Making a graph: Now, you will use the data you have added to the skill sheet to make a graph. 

a. Use your mouse to highlight the titles and data in columns A and B. 

b. Then, go to Insert and click on Chart. 

c. In step 1 of the chart wizard, choose the XY (Scatter) format for your chart and click “Next.” 

d. In step 2 of the chart wizard, you will see a graph of your data. Click “Next” again to get to step 3. Here 

you can change the appearance of the graph. 

e. In step 3 of the chart wizard, add titles and uncheck the show legend-option. In the box for the chart title 

write “Temperature vs. Time.” In the box for the value x-axis, write “Time (seconds).” In the box for the 

value for y-axis, write “Temperature (deg Celsius).” 

2.2

Page 2 of 3 

f. In step 4 of the chart wizard, click the option to show the graph as an object in Sheet 2. At this 

point you will finish your work with the chart wizard. 

g. Setting the scale on the x-axis: Place the cursor on the x-axis and double click. Set the 

minimum of the scale to be 0, the maximum to be 310. Set the major unit to be 100 and the minor unit to 

be 20. Then, click OK. Note: Make sure the boxes to the left of the changed values are NOT checked. 

h. Setting the scale on the y-axis.: Place the cursor on the y-axis and double click. Set the minimum of the 

scale to be 20, the maximum to be 41. Set the major unit to be 10 and the minor unit to be 2. Then, click 

OK. Note: Make sure the boxes to the left of the changed values are UNchecked. 

i. You are now finished with your graph. It is located on Sheet 2 of your spreadsheet. 

3. Performing calculations: 

a. Return to Sheet 1 of your spreadsheet. 

b. The third column of data, “Slope,” will be filled by performing a calculation using data in the other two 

columns. 

c. Highlight the second cell from the top in the Slope column (cell C2). Type the following and hit enter: 

= (B3-B2)/(A3-A2) 

Explanation of the formula: The equal sign (=) indicates that the information you type into the cell is a 

formula. The formula for the slope of a line is as follows. Do you see why the formula for cell C2 is 

written the way it is? 

y2 – y1 slope = 

--------------x2 

– x1 d. Adding the formula to all the cells: Highlight cell C2, then drag the mouse down the column until the 

cells (C2 to C11) are highlighted. Then click Edit, then Fill, then Down. The formula will copy into 

each cell in column C. However, the formula pattern will be appropriate for each cell. For example, the 

formula for C2 reads: = (B3-B2)/(A3-A2). The formula for C3 reads: = (B4-B3)/(A4-A3). Note: The 

“=” sign is important. Do not forget to add it to the formula. 

e. In column C, you will see the slope for pairs of data points. Now, answer the questions below. 

1. Which is the independent variable—time or temperature? Which is the dependent variable? 

2. When setting up the data in a spreadsheet, which data set goes in the first column, the independent variable 

or the dependent variable? 

3. Use the graph you created in step 2 of the example to describe the relationship between temperature and the 

time it takes to heat up a volume of water. 

4. Look at the values for slope. How do these values change for the graph of temperature versus time? 

2.2

Page 3 of 3 

5. The following data is from an experiment in which the temperature of a substance was taken as it 

was heated. Transfer this data into a spreadsheet file and make an XY(Scatter) graph. 

Time (seconds) 

Independent data 

Temperature (°C) 

Dependent data 

10 7.5 

20 10.8 

30 11.6 

40 11.9 

50 13.3 

60 21.9 

70 26.3 

80 26.6 

90 29.1 

100 31.1 

6. Use the following data set to make a graph in a spreadsheet program. Find the slope for pairs of data points 

along the plot of the graph. Is the slope the same for every pair of points? 

Independent 

data 

Dependent 

data 

1 5 

2 7 

2.5 8 

3.2 9.4 

1.5 6 

0.5 4 

4 11 

2.8 8.6 

4.2 11.4 

5 13 

2.2

Name: Date: 

2.2 Identifying Control and Experimental Variables 

An experiment is a situation set up to investigate relationships between variables. In a simple ideal experiment 

only one variable is changed at a time. You can assume that changes you see in other variables were caused by 

the one variable you changed. The variable you change is called the experimental variable. This is usually the 

variable that you can freely manipulate. For example, if you want to know if the mass of a toy car affects its 

speed down a ramp, the experimental variable is the car’s mass. You can add “cargo” to change the mass of car. 

The variables that you keep the same are called control variables. In the toy car experiment, control variables 

include the angle of the ramp, photogate positions, and release technique. 

Use this skill sheet to practice identifying control and experimental variables. 

• Alex is studying the effect of sunlight on plant growth. His hypothesis is that plants that are exposed to 

sunlight will grow better than plants that are not exposed to sunlight. In order to test his hypothesis, he 

follows the following procedures. He obtains two of the same type of plant, puts them in identical pots with 

potting soil from the same bag. Then he puts one plant in the sunlight and the other in a dark room. He 

waters the plants with 200 mL of water every other day for two weeks. 

Solution: 

The experimental variable in the experiment is the light exposure of the plant. One plant is put in sunlight 

and the other is put in darkness. The control variables are the type of plant, the pot, the soil, amount of water, 

and the time of the experiment. 

1. Julie sees commercials for antibacterial products that claim to kill almost all the bacteria in the area that has 

been treated with the product. Julie asks, “How effective is antibacterial cleaner in preventing the growth of 

bacteria?” She sets up an experiment in order to study the effectiveness of antibacterial products. Julie 

hypothesizes that the antibacterial soap will prevent bacterial growth. In her experiment, she follows the 

following procedure. 

a. Obtain two Petri dishes with nutrient agar. 

b. Rub a cotton swab along the surface of a desk at school. Then, carefully rub the nutrient agar with the 

cotton swab without breaking the gel. 

c. Repeat the same process with the other Petri dish. 

d. Spray one of the Petri dishes with an antibacterial kitchen spray. 

e. Carefully tape shut both of the Petri dishes and place them in an incubator. 

f. Check the Petri dishes and record the results once a day for one week. 

Identify the experimental variable and three control variables in the experiment. 

2.2

Page 2 of 2 

2. John notices that his mom waters the plants in their house every other day. He asks, “Will plants 

grow if they are not watered regularly?” He hypothesizes that plants that are not watered regularly 

will not grow as large as plants that are watered regularly. In order to test his hypothesis, he 

conducts the following experiment. 

a. Obtain two healthy plants of the same variety and size. 

b. Plant each plant in the same type of pot and the same brand of potting mix. 

c. Place both plants in the same window of the house. 

d. Water one of the plants every other day with 250 mL of water. 

e. Water the other plant once a week with 250 mL of water. 

f. Measure the height of the plants once a day for one month. 


3. Mike’s dad always buys bread with preservatives because he says it lasts longer. Mike asks, “Will bread with 

preservatives stay fresh longer than bread without preservatives?” He hypothesizes that bread with 

preservatives will not grow mold as quickly as bread without preservatives. In order to test his hypothesis, he 

conducts the following experiment. 

a. Obtain one slice of bread containing preservatives and one slice of bread without any preservatives. 

b. Dampen two paper towels. Fold the paper towels so that they will lay flat inside a zipper-top bag. 

c. Lay each paper towel inside a separate zipper-top bag. 

d. Place one slice of bread in each bag and seal the bags. 

e. Place bags with bread and paper towels in a dark environment for one week. 

f. Record mold growth once a day for one week. 


4. In science class, Kathy has been studying protists. She has been learning specifically about protists called 

algae that live in ponds. She knows that algae thrive when there are plenty of nutrients available for them. 

Kathy asks, “Will water that has been treated with fertilizer have more algae than water that has not been 

treated with fertilizer?” In order to test her hypothesis, Kathy does the following experiment. 

a. Obtain a sample of algae from the teacher. 

b. Obtain two beakers with 500 mL of water in each beaker. 

c. Put one teaspoon of plant fertilizer in one of the beakers. 

d. Put an equal amount of algae sample in each of the beakers. 

e. Place the beakers in a sunny window for two weeks. 

f. Using a microscope, examine algae growth in each of the beakers every other day for the two weeks and 

record your results. 


2.2

Name: Date: 

3.1 Position on the Coordinate Plane 

To describe any location in two dimensions, we use a grid called the coordinate plane. You can describe any 

position on the coordinate plane using two numbers called coordinates, which are shown in the form of (x, y). 

These coordinates are compared to a fixed reference point called the origin. The table below describes the x and 

y coordinates: 

Your home is at the origin, and a park is located 2 miles north and 1 mile east of your home. 

• Show your home and the park on a coordinate plane, and give the coordinates for each. 

• After you go to the park, you drive 2 miles east and 1 mile north to the grocery store. What are the 

coordinates of the grocery store? 

Solution 

If your home is at the origin, it is given the coordinates 

(0, 0). By counting over 1 box from the origin in the 

positive x-direction and up 2 boxes in the positive 

y-direction, you can place the park on the coordinate 

plane. The park’s coordinates are (+1 mile, +2 miles). 

From the park, count over 2 more boxes in the positive 

x-direction and up one more 1 box in the positive 

y-direction to place the grocery store. That makes the 

grocery store’s coordinates (+3 miles, +3 miles). 

_ 

Coordinate Which axis is it on? Which is the positive 

direction? 

Which is the negative 

direction? 

x horizontal, called the x-axis right or east left or west 

y vertical, called the y-axis up or north down or south 

1. You are given directions to a friend’s house from your school. They read: “Go east one block, turn north and 

go 4 blocks, turn west and go 1 block, then go south for 2 blocks.” Using your school as the origin, draw a 

map of these directions on a coordinate plane. What are the coordinates of your friend’s house? 

2. A dog starts chasing a squirrel at the origin of a coordinate plane. He runs 20 meters east, then 10 meters 

north and stops to scratch. Then he runs 10 meters west and 10 meters north, where the squirrel climbs a tree 

and gets away. 

a. Draw the coordinate plane and trace the path the dog took in chasing the squirrel. 

b. Show where the dog scratched and where the squirrel escaped, and give coordinates for each. 

3. Does the order of the coordinates matter? Is the coordinate (2, 3) the same as the coordinate (3, 2)? Explain 

and draw your answer on a coordinate plane. 

3.1

Name: Date: 

3.1 Latitude and Longitude 

History: Latitude and longitude are part of a grid system that describes the 

location of any place on Earth. When formalized in the mid-18th century, the 

idea of a grid system was not a new one. More than 2000 years ago, ancient 

Greeks drew maps with grids that looked much like our maps today. Using 

mathematics and logic, they postulated that Earth could be mapped in degrees 

north and south of the Equator and east and west of a line of reference. From 

the ancient times, geographers and navigators used devices such as the crossstaff, 

astrolabe, sextant, and astronomical tables to determine latitude. But 

determining longitude required accurate timepieces, and they were not reliably 

designed until the 1700’s. 

Latitude: Think of Earth as a transparent sphere, just as the ancient Greeks 

did. Now imagine yourself standing so that your eyes are at the center of that 

sphere. If you tip your head back and look straight up, you will see the North 

Pole above you. If you look straight down, you will see the South Pole below 

you. If you turn around while looking straight out at the middle of the sphere, your eyes will follow the Equator, 

the line around the middle of Earth. The ancient Greeks realized that they could describe the location of any place 

by using its angle from the Equator as measured from that imaginary place at the center of Earth. 

All latitude lines run parallel to the Equator, creating circles that get smaller and smaller until they encircle the 

Poles. Because latitude lines never intersect, latitude lines are sometimes referred to as parallels. 

At first, you might be confused because when latitude lines are placed on a map. They 

appear to run from the left side of the page to the right. You might think they measure 

east and west, but they don't. The graphic at the right shows latitude lines. If you think 

of them as steps on a ladder, then you will see the lines are taking you “up” toward the 

north or “down” toward the south. (Of course, there is no real “up” or “down” on a 

map or globe, but the association of LAdder and LAtitude may help you.) 

The Equator is designated as 0º. The North Latitude lines measure from the Equator 

(0º) to the North Pole (90ºN). The South Latitude lines measure from the Equator (0º) 

to the South Pole (90ºS). There are other special latitude lines to note. The Tropic of 

Cancer is at 23.5ºN latitude, and at 23.5ºS latitude is the Tropic of Capricorn. These lines represent the farthest 

north and farthest south where the sun can shine directly overhead at noon. Latitudes of 66.5º N and 66.5º S mark 

the Arctic and Antarctic Circles, respectively. Because of the tilt of the Earth, there are winter days when the Sun 

does not rise and summer days when the sun does not set at these locations. 

Longitude: Now imagine yourself back in the transparent sphere. Look up at the 

North Pole and begin to draw a continuous line with your eyes along the outside of the 

sphere to the South Pole. Turn to face the opposite side of the sphere and draw a line 

from the South Pole to the North Pole. These lines, and all other longitude lines, are 

the same length because they start and end at the poles. Look at the graphic below and 

see that although longitude lines are drawn from north to south, they measure distance 

from east or west. 

3.1

Page 2 of 4 

There are no special longitude lines, so geographers had to choose one 

from which to measure east and west. Longitude lines are also called 

3.1 

meridians, so this special line is called the Prime Meridian and is labeled 

0º. The ancient Greeks chose a Prime Meridian that passed through the 

Greek Island of Rhodes. In the 1700's, the French chose one that passed 

through Ferro, an island in the Canary Islands. There are maps that show 

that America even used Philadelphia as their special reference location. 

But in 1884, the International Meridian Conference met in Washington, 

DC. They chose to adopt a Prime Meridian that passes through an 

observatory in Greenwich, England. At the same conference, they also 

determined a point exactly opposite of the Prime Meridian. This second 

important longitude line is the 180º meridian. Longitude lines measure eastward and westward from the Prime 

Meridian (0º) to the180º meridian. Superimposed on the 180º meridian is the International Dateline. This special 

line does not follow the 180º meridian exactly. It zigzags a bit to stay in the ocean, which is an unpopulated area. 

International agreements dictate that the date changes on either side of the Dateline. 

GPS and decimal notations. In the past, latitude and longitude lines always had measurement labels of degrees 

(º), minutes ( ' ), and seconds ( "). The labels of “minutes” and “seconds” did not denote time in these cases. 

Instead they described places between whole degrees of longitude or latitude more exactly. For example, 

consider Sacramento, CA. Traditionally, its location was said to be at 38º 34' 54"N (38 degrees, 34 minutes, 

54 seconds North) and 121º 29' 36"W (121 degrees 29 minutes, 36 seconds West). Now GPS (Global Positioning 

System), in decimal notation would say Sacramento is located at 38.58ºN and 121.49ºW. Note: As a matter of 

custom when giving locations, latitude is listed first and longitude second. 

Finding a Location on a Globe 

You can find any location by using latitude and longitude on a globe. See the 

example in the diagram. The position is 70ºN and 40ºW. First on the globe, you 

would find the latitude line 70ºN, seventy degrees north of the Equator. Next you 

would find the longitude line 40ºW, forty degrees west of the Prime Meridian. Trace 

the lines with your fingers. Where they intersect, you will find the location. In this 

case, you have located Greenland. 

Finding a Location on a Map 

You use the same procedure to find any location on a map. Look at the graphic 

below. The position is 10ºS and 160ºE. First you would find the latitude line 

10ºS, ten degrees south of the Equator. Next you would find the longitude 

160ºE, one hundred-sixty degrees east of the Prime Meridian. You have 

located the Solomon Islands.

Page 3 of 4 

Use an atlas or globe to answer these practice questions. 

1. What country will you find at the following latitude and longitude? 

a. 65ºN 20ºW 

b. 35ºN 5º E 

c. 50º S 70ºW 

d. 20ºS 140ºE 

e. 40ºS 175ºE 

2. What body of water will you find at the following latitude and longitude? 

a. 20ºN 90ºW 

b. 40ºN 25ºE 

c. 20ºN 38º E 

d. 25ºN 95ºW 

e. 0ºN 60ºW 

Converting Traditional Notation To Decimal Notation 

Sometimes you need to convert the traditional notation of degrees, minutes, and seconds into decimal notation. 

First you must understand this traditional notation, which was a base-60 system. 

Let's look at 34º 15' (thirty-four degrees 15 minutes). 

One degree = 60 minutes 

One minute = 60 seconds 

One degree = 3,600 seconds (60 × 60) 

Regardless of the system, the notation will begin with 34 degrees. To change the minutes into a decimal, you 

must divide 15 by 60, the number of minutes in one degree (15/60). The answer is 0.25. Therefore, the decimal 

notation would be 34.25º or thirty-four and twenty-five hundredths degrees. 

Let's look at 12º 20' 38" (twelve degrees, twenty minutes, thirty-eight seconds). We know the notation will begin 

with 12 degrees. Next we have to convert the 20 minutes into seconds (20 × 60 = 1,200 seconds. Then we add the 

38 seconds for a total of 1,238 seconds. There are 3,600 seconds in one degree, so you must divide 1,238 by 

3,600. (1,238 / 3,600). The answer is 0.34. Therefore the decimal notation would be 12.34º or twelve and thirtyfour 

hundredths degrees. 

3.1

Page 4 of 4 

3. Convert the following latitudes in traditional notation to decimal notation. (Round your answer to 

the nearest hundredth.) 

a. 30º 20' N 

b. 45º 45' N 

c. 20º 36' 40" S 

d. 60º 19' 38" S 

4. Convert the following longitudes in traditional notation to decimal notation. (Round your answer to the 

nearest hundredth.) 

a. 25º 55' E 

b. 145º 15' E 

c. 130º 37' 10" W 

d. 85º 26' 8" W 

3.1

Name: Date: 

3.1 Map Scales 

Mapmakers have developed a tool that allows them to accurately draw the entire world on a single piece of paper. 

It’s not magic—it’s drawing to scale. To be useful, maps must be accurately drawn to scale. The mapmaker must 

also reveal the scale that was used so that a map-reader can appreciate the larger real-life distances. The scale is 

usually written in or near the map’s legend or key. 

There are three kinds of map scales: fractional, verbal, and bar scales. A fractional scale shows the relationship of 

the map to actual distance in the form of a fraction. A scale of 1/100,000 means that one centimeter on the map 

represents 100,000 centimeters (or 1 kilometer) of real life distance. 

A verbal scale expresses the relationship using words. For example, “1 centimeter equals 500 kilometers.” This is 

a more usable scale, especially with large real-life distances. With a scale of 1 cm = 500 km, you could make a 

scale drawing of North America on one piece of paper. 

A bar scale is the most user-friendly scale tool of all. It is simply a bar drawn on the map with the size of the bar 

equal to a distance in real life. Even if you do not have a ruler, you can measure distances on the map with a bar 

scale. Just line up the edge of an index card under the bar scale and transfer the vertical marks to the card. Label 

the distances each mark represents. You can then move the card around your map to determine distances. You 

might wonder what you should do if a location falls between the vertical interval lines. You must use estimation 

to determine that distance. Be careful to look at the scale before estimating. For example, if the distance falls 

half-way between the 10 and the 20 kilometer scale marks, estimate 15 kilometers. If the scale is different and the 

distance falls half-way between 30 and 60 kilometer marks, you must estimate 45 kilometers. 

Let’s explore the different kinds of scales. You will need centimeter graph paper, plain paper, an index card, and 

a centimeter ruler or measuring tape for these activities. 

Fractional scale 

Materials: Graph paper 

Trace a simple object on a piece of graph paper. (A large paper clip, pen, small scissors, or paperback book works 

well.) Now make a scale drawing of the object using the fractional scale of 1/4. (Remember this means that for 

every 4 blocks occupied in the original tracing, you will have only one block on the scale drawing.) Be sure to 

label the scale on the finished scale drawing. 

3.1

Page 2 of 3 

Verbal scale 

Materials: Centimeter graph paper and centimeter measuring tape or ruler. 

You are going to make a scale drawing of a person. Ask a classmate to stand against a wall with his/her arms 

outstretched to the side. Take 4 measurements in centimeters: 1) Distance from top of head to floor. 2) Distance 

from right finger tip to left finger. 3) Distance from top of head to shoulders. 4) Distance from shoulders to waist. 

Write the verbal scale of “1 cm equals 10 cm” on the bottom of a piece of centimeter graph paper. On that paper 

translate the measurements that your took into a simple figure drawing of your classmate. (Remember if a 

measurement is 25 centimeters in real life, you will have to make a drawing that is within 2 ½ centimeter blocks 

of the graph paper.) 

Bar scale 

Materials: Plain paper and centimeter ruler or tape. 

Position the paper so that it is wider than it is long. 

Draw a bar scale that is a total of 6 centimeters long at bottom of the paper. Make four vertical marks at 0 cm, 

2 cm, 4 cm, and 6 cm. Write “0”over the first mark, “50” over the second, “100” over the third and “150” of the 

last mark. Underneath the bar write “Kilometers.” Mark “N” for north at the top of your paper. Now use your 

imagination to draw an island (of any shape) that is 450 miles long and 200 miles wide at its widest point. Draw 

a star to mark the capital city, which is located on the northern coast 100 miles from the west end of the island. 

1. Answer these questions about Andora and Calypso: 

a. Which island appears bigger? 

b. Can you tell whether you can ride a bike in one day 

from point A to point B on either map? If no, why not? 

c. Measure the distance from the center of the dot to the 

right of A to the center of the dot to the left of B on 

both maps. Are the measurements the same? 

d. If the measurements are the same on both maps, does 

that mean the distance from point A to point B is the 

same on both maps? Explain your answer. 

e. Let’s write in the scale for these two islands. Write the scale of 1cm = 5 km on Andora. Write the scale 

of 1 cm = 1000 km on Calypso. Now answer the question, which island is bigger? 

2. On the next page is a map of Monitor Island. Use the bar scale to find distances on this island. Assume that 

you are measuring “as the crow flies.” That means from point to point by air because there are no roads to 

follow. Always measure from dot to dot, and be sure to label your answers in kilometers. 

a. Point L to Point M 

b. Point Y to Point Z 

c. Point Z to Point P 

d. Point P to Point M 

e. Point Q to Point T 

3.1

Page 3 of 3 

f. Point Q to Point M 

g. Point T to Point M 

h. Point Z to Point P to Point X 

i. Point X to Point L to Point M 

j. Point X to Point P to Point Z to Point Y 

Bonus: Measure around the coast of Monitor Island. It’s hard to be exact, but write your best estimate. 

3.1

Name: Date: 

3.1 Navigation Project 

Nautical charts have long been used by ship captains to navigate the oceans. As land has been increasingly 

developed and harbors built, more and more information is needed to safely navigate near shore. Additionally, 

offshore shallow banks, reefs, islands, seamounts, and other obstructions needed to be identified so that they 

don’t hinder the passage of boats. 

In this project, you and two other captains will navigate through the waters around Puerto Rico and some of the 

Virgin Islands using three real nautical maps. Your journey includes a stop at Isla de Vieques, which was a US 

Navy testing ground for bombs, missiles, and other weapons. It was vacated in May 2003 and now is used by 

locals and tourists. Bon Voyage. 

Materials: 

• NOAA map #25640 

(laminated) 

• NOAA map #25641 

(laminated) 

• NOAA map #25647 

(laminated) 

Getting started: 

1. Have all three maps accessible. 

2. Before beginning your imaginary journey, spend some time studying the maps. Look at any legends 

(example: note on pipelines and cables), abbreviation lists, and Notes (such as Note E on map 25640). Look 

at the map scale. Note whether the soundings are in fathoms or feet. 

3. Note that the maps are laminated, so you can use an erasable marker to outline your path. 

Making predictions: 

Note: 

Laminated maps are 

available from NOAA 

(www.noaa.gov) or 

boating/marine supply 

stores, as well as some 

Coast Guard Stations. 

• Internet access 

• Erasable overhead 

projector marker 

a. What kind of ecosystem do you expect to find in these warm, sunlit waters? 

b. What does this mean about navigating this area? 

3.1

Page 2 of 5 

It’s time to go! 

3.1 

1. You and your two partners are tri-captains on a boat that is 12 feet deep. On board, you have a 

small row boat. Besides your clothes and toiletries for the trip, you will bring along wading boots, a solar 

still, a radio, your three maps, water, and food. 

2. You will be traveling from the west coast of Puerto Rico, eventually ending your trip on the island of St. 

John. As captains, you will be making decisions about the course the boat will be taking based on directions 

given below. You will need to look out for (among other things) shallow water, pipelines, and other 

obstructions. Listen to what the map is telling you. 

3. Let’s start with map 25640. What is the scale of this map? 

4. What does that mean? 

5. How many feet are there in a fathom? Hint: The answer is outside the border of the map. 

6. Find Punta Higuero on the west coast of Puerto Rico. What is located here? Use your abbreviations. You 

will probably have to look it up. 

7. You will now be moving south along the west coast and then the south coast of Puerto Rico. Notice the light 

blue area around the coast. At the seaward edge of this area is a line. Every few inches along this line, you 

will see a number 10. What this means is that anywhere along this line the depth of the water is 10 fathoms. 

Remember, your boat is 12 feet deep. How many fathoms is this? 

8. So your boat is fine anywhere along the line. However, as you head toward the coast from this 10-fathom 

line, the depth decreases, but since the depth is not marked again, you do not know how quickly it decreases 

and thus can't take your boat any closer to the shore. Remember this as you travel. So start traveling south. 

What do you encounter near the Bahia de Mayaguez? 

9. What does this mean? 

10. Is the depth of the water still suitable for traveling? 

11. Travel around the marine conservation district. Should anyone be fishing here? 

12. Can you pass between Bajas Gallardo and the Marine Conservation District? If so, trace the path through 

and if not, find another way around towards the south shore. 

13. Stay near to shore so you can have great views of the beautiful shallow blue waters. Find Punta Cayito and 

Punta Barrancas on the south shore. In the area offshore, there is a section between the 10 fathoms line and 

the next depth line of 100 fathoms were there are several abbreviated notations. Name three by noting the 

abbreviation and what it means. 

14. Find the lighthouse near Cayos de Ratones. What type of lighthouse is it and why is that different than 

occulting? 

15. 5M means that it can be seen for 5 nautical miles, which is 1.852 kilometers or 1.15 miles. 

16. As you travel towards the southeastern coast of Puerto Rico, what area in a square dashed purple box do you 

see? 

17. Do you think it would be a good or bad idea to drop anchor there?

Page 3 of 5 

18. Head to Isla de Vieques. There are supposed to be two beautiful bays that are filled with organisms 

that are bioluminescent. These one-celled organisms give off a blue-green glow when disturbed. 

You'll have to wait here until night-time in order to see this natural wonder. Can you take your 

ship right up to the shore? If not, what can you do to get there? 

19. How many lighthouses are there on the Island? 

20. Two lighthouses are flashing. One is occulting. What is the fourth, what does the symbol mean, and what 

two colors are associated with it? 

21. How far out can you see the flashing and occulting lighthouse lights on the Island? 

22. Your next stop is Savana Isle, a small island just west of St. Thomas. As you travel in that direction, what do 

you notice there are many of in the area of the Virgin Passage? 

23. What does that mean you should NOT do in this area? 

24. Can you bring your boat in directly to Savana Isle? 

25. What does the (269) mean? 

26. Now you are going to move to map 25641. The soundings are done in what units? 

27. Orient yourselves for a minute. You are currently at Savana Isle. Find it on the map. 

28. What is the scale on this map? 

29. You can see that the scales on the maps are quite different. What do you notice when you look at the maps 

themselves. How are they different? 

30. When you are sailing in this area, where do you call to report spills of oil and hazardous substances? There 

are two choices. 

31. For weather information, to what station do you tune? 

32. From Savana Isle, head toward Cricket Rock using Salt Cay or Dutchcap Passage. How many fathoms deep 

is the coastline? 

33. Should you anchor and row in or go right up to the shore? 

34. How much rock is covered and uncovered? 

35. What are the local bottom characteristics? 

36. By the way, what is a cay? 

3.1

Page 4 of 5 

37. Now you will head to White Horseface Reef at 

Hans Lollik Isle. Watch your depths as you 

travel in that direction. What is submerged en 

route to the Isle? 

38. Anchor where you can and spend some time 

snorkeling. Once you have completed your 

swim and returned to the ship, start heading 

through the Leeward Passage. Move to map 

25647 at this point. In what units are the 

soundings measured? 

39. What is the scale? 

40. Once again, what do you notice about the scale and amount of detail in the map? 

41. On this map, what do the green solid and dashed green lines represent? 

42. How does that affect your boat? 

43. Heading through Leeward Passage and south of Thatch Cay, there is a rectangular box with a blue tint in the 

waterway. It is there to let you know, as captains, that there is an obstruction, a fish haven, which is an 

artificial reef. These are usually made of rock, concrete, car bodies, and other debris. If you'll notice, inside 

the box, it states an authorized minimum depth of 60 feet. If you look at the depth of the water on the map 

around the box, the values are deeper than 60 feet. Because of the artificial reef, the map is telling you that 

you can be assured to not have any obstruction down to 60 feet, but it is hazardous after that depth. The 

minimum depth is checked by sweeping the area with a length of horizontal wire. If there is an obstruction, 

the wire would get snagged. Is your boat okay to travel through this area? 

44. Continue to Cabrita Point and through to St. James Bay. You are headed towards Jersey Bay, but you are 

going to have to be very careful navigating the Jersey Bay area as you will then head into Banner Bay 

Channel. It is recommended by the map that you seek local knowledge about some broken piles (wooden 

columns driven into the harbor sand beds on which structures can be built in the water) which may be below 

the waterline and are not marked on the map. As you look at the channel, make note of the depth of the 

water. Will you be able to take your boat in or row in? How can you tell? 

45. Bring your wading boots just in case you need them. The symbols that look like ties (colored in green and 

purple) will help you navigate your way. These are buoys. The first letter of each buoy is either an R for ‘red’ 

or G for ‘green.’ The rule of thumb is to keep red buoys to the right (starboard) when returning to a harbor 

and green buoys to the left (port). Using that rule, get yourself to the coast and have some lunch in town, 

especially after all that rowing. 

3.1

Page 5 of 5 

46. Take a taxi ride west of the harbor to the 

mangrove lagoon. Can you wade in there with 

your boots? 

47. Mangroves are trees and shrubs that grown in 

saline marine areas. The mangrove roots impede 

the water flow. Since the water is carrying 

sediment, the slowed water deposits the sediment 

over time and actually builds coastline. These are 

very special ecosystems. 

48. Spend some time here, take the taxi back to the 

row boat, and get back to your ship. 

49. Find a path to St. John and choose a landing site. Describe three more nautical notations that you encounter 

and how they influenced your route. 

50. Congratulations! Your voyage has ended. Hope you learned how important map reading is for nautical 

navigation. Show your teacher your route. 

3.1

Name: Date: 

4.1 Vectors on a Map 

You have learned that velocity is a vector quantity—this means that when you talk about velocity, you must 

mention both speed and direction. You can use velocity vectors on a coordinate plane to help you figure out the 

position of a moving object at a certain point in time. 

Your home is at the origin. From there you ride your bicycle to the movie theater. You ride 30. km/hr north for 

0.50 hour, and then 20. km/hr east for 0.25 hours. 

Show your home and the movie theater on a coordinate plane, and give the coordinates for each. 

Solution: 

If your home is at the origin, it is given the coordinates 

(0, 0). To find the position of the movie theater, you need 

to find the change in position. Use the relationship: 

change in position = velocity × change in time 

First change in position: +30. km/hr × 0.50 hr = 15 km 

NORTH 

Second change in position: +20. km/hr × 0.25 = 5 km 

EAST 

From home, travel north 15 km. Then turn and go east 5 km. 

The coordinates of the movie theater are ( +5 km, +15 km). 

Note: Be careful to report the x-coordinate first. It does not matter which direction you traveled first. When 

reporting position, you always give the x- (east-west) coordinate first, then the y- (north-south) coordinate. 

1. Augustin and Edson are going to a baseball game. To get to the stadium, they travel east on the highway at 

120. km/hr for 30. minutes. Then they turn onto the stadium parkway and travel south at 60. km/hr for 

10. minutes. Assume their starting point is at the origin. What is the position of the stadium? 

2. Destiny and Franijza are at the swimming pool. They decide to walk to the ice cream shop. They walk north 

at a pace of 6 km/hr for 20. minutes, and then east at the same pace for 10. minutes. If the swimming pool is 

at the origin (0,0) what is the position of the ice cream shop? 

3. After finishing their ice cream, the girls decide to go to Destiny’s house. From the ice cream shop, they walk 

south at a pace of 4.0 km/hr for 15 minutes. What is the position of Destiny’s house? 

4. Draw a map showing the swimming pool at the origin (0,0). Show the coordinates of the ice cream shop and 

Destiny’s house. 

5. Challenge! Make up your own velocity question. Your object (or traveler) should make at least one turn. 

Use at least two different speeds in your problem. Trade questions with a partner. Use a coordinate plane to 

help you solve the new question. 

4.1

Name: Date: 

3.2 Topographic Maps 

Flat maps can easily show landmasses and political boundaries. However, mapmakers need to draw special 

maps, called topographic maps, to show hills, valleys, and mountains. Mapmakers use contour lines to show the 

elevation of land features. The 0 contour line refers to sea level. The height above sea level is measured in equal 

intervals. Always look at the legend to see the elevation of each contour line interval. Sometimes these contour 

lines describe an increase of 20 feet. On other maps, especially those showing mountains, the contour lines may 

show elevation intervals of 100 to 1000 feet. 

• Contour lines and elevations 

Look at Figure 1. On this map, the contour interval is 100 feet. Let’s look 

at the letters marked on the map. Point A is at sea level. That means it is on 

the 0 contour line all the way around the island. Point B is on the next 

contour line. That means that B is 100 feet above sea level. What is the 

elevation at Point C? If you said 200 feet, you would be correct. At what 

elevation is Point D? The correct answer is somewhere between 0 and 100 

feet. You can’t be exact because D is not on a contour line. Where is Point 

E? Yes, it’s at sea level, the same level as A. 

Take a minute to color the contour key and the map. Color green between 0 and 100 feet, color yellow 

between 100 and 200 feet, color red between 200 and 300 feet. Mapmakers generally use blue for water 

only, so do not use it in a contour key. 

• Profile Maps 

You can also translate contour lines into a profile map. In this way you can 

actually draw what you would see if you were approaching by sea. Look at 

the following map as you read the steps to create a profile map. First, you 

draw a graph above the map that shows the intervals. The contour is 20 

feet so you would label the elevation in 20-foot intervals on the left. Your 

task is to make dots on the lines of the graph directly above the island 

contour lines. Put a ruler against the left hand edge of the island, and make 

a dot on the 0' line of the graph. Slide your ruler to the right hand edge of 

the island and make a second dot on the 0' line. Next go to the second 

contour line and mark two dots on the 20-foot interval line in the graph 

above the map. Continue marking two dots at the widest dimensions for 

contour lines 40 feet and 60 feet. Now connect the dots. This shows you 

the profile of the island. Note, the island’s elevation is probably a little more than 60 feet, so you could draw 

a peak on the top of the hill taller than 60 but less than 80 feet. Even if the island were 79 feet tall, there 

would not be an 80-foot contour line. 

3.2

Page 2 of 3 

1. Draw a profile map of the island in Figure 3. (Hint: You will have four dots on the 20' line.) 

2. Reverse the process to make a topographic map from the profile map. For each dot on the graph, you will 

make a small dot on the map showing where the contour line begins or ends. Draw a free form contour line 

that runs through the two dots. The 0' contour (sea level) has been done for you. 

3.2

Page 3 of 3 

3. Color the following map and contour key, and answer the questions. 

a. What is the lowest elevation on this map? _______ 

b. What is the highest elevation on this map? _______ 

c. What is the elevation at X? _______ 

d. What is the elevation at Y? _______ 

e. What is the elevation at Z? _______ 

4. Today scientists worry that global warming may cause the ice caps to melt, causing the sea levels to rise. 

Look at the map below. It has a contour of 15 feet. 

a. Let’s pretend that the sea level has risen 15 feet. Color the first contour (0–15') of the map dark blue, so 

that the new sea level is revealed. How has this island changed? 

b. Now let’s pretend that the sea level rises another 15 feet. Color the next contour light blue and describe 

the changes in the original island. 

c. What if the sea level rose by 30 feet due to global warming, and a hurricane hit the island? Could the 

people find dry land if there were a 35-foot storm wave? 

3.2

Name: Date: 

3.3 Bathymetric Maps 

Imagine that all the water in the oceans disappeared. If this happened, you would be able to see what the bottom 

of the ocean looks like. Fortunately, we don’t have to drain water from the ocean to get a picture of the ocean 

floor. Instead, scientists use echo sounding and other techniques to “see” the ocean floor. The result is a 

bathymetric map. This skill sheet will provide you with the opportunity to practice reading a bathymetric map. 

Main features on a bathymetric map 

1. Main features on a bathymetric map are mid-ocean ridges, rises, deep ocean trenches, plateaus, and fracture 

zones. Find one example of each of these on a bathymetric map. 

a. Mid-ocean ridge:____________________ 

b. Rise: ____________________ 

c. Deep ocean trench: ____________________ 

d. Plateau: ____________________ 

e. Fracture zones: ____________________ 

2. All the ridges you see on the bathymetric map behave in the same way even though they may not be in the 

middle of an ocean. What happens at mid-ocean ridges? 

3. Find the Rio Grande Rise on the bathymetric map. Then, find the East Pacific Rise. 

a. Which of these features is an example of a mid-ocean ridge? 

b. Find another example of a rise that is a mid-ocean ridge. Justify your answer. 

c. Find another example of a rise that is not a mid-ocean ridge. Justify your answer. 

4. There are a number of deep ocean trenches on the western side of the North Pacific Ocean. What process is 

going on at these trenches? 

5. What plate tectonic process probably caused the fracture zones in the North Pacific Ocean? Justify your 

answer. 

How is the East Pacific Rise different from the Mid-Atlantic Ridge? 

6. Look carefully at the Mid-Atlantic Ridge. Describe what this ridge looks like. Be detailed in your 

description. 

7. Now, look carefully at the East Pacific Rise. Describe what this ridge looks like. Be detailed in your 

description. 

8. Which of these features has a noticeable dark line running along the middle of the feature? Look at the 

legend at the bottom of the map. What does this dark line indicate? 

3.3

Page 2 of 2 

9. Based on your observations of these two features, draw a cross-section of each in the boxes below. 

Mid-Atlantic Ridge cross-section East Pacific Rise cross-section 

10. One of these mid-ocean ridges has a very fast spreading rate. The other has a very slow spreading rate. 

Which one is which? Justify your answer based on your answer to questions 8 and 9. 

3.3

Page 1 of 2 

3.3 Tanya Atwater 

Tanya Atwater is a professor of Earth Science at the University of California, Santa Barbara. She 

has studied sea floor spreading and propagating rifts. She is currently researching the plate tectonic history 

of western North America. One of her main goals as a geologist is to educate people about our Earth. 

Artist and adventurer 

While growing up, Tanya 

Atwater wanted to be an 

artist. She loved figuring 

out how to record on paper 

the things she could see in 

three dimensions. 

Atwater and her family 

went on many vacations, 

where, she says, “I always 

hogged the maps, taking 

great pleasure in translating 

between the paper map and the passing countryside.” 

Whether it was camping, hiking, or river rafting, all of 

the trips had one thing in common—adventure. As a 

result, Atwater developed a deep love for the 

outdoors. 

Geology in the mountains and at sea 

Atwater started her college career at the 

Massachusetts Institute of Technology (MIT). She 

tried a variety of majors, including physics, chemistry, 

and engineering. Atwater then attended the Indiana 

University geology summer field camp in Montana. 

There, she learned about geological mapping and how 

land structures translate into lines and symbols. 

Atwater was hooked on geology! 

Atwater transferred to the University of California at 

Berkley. She had already completed many math and 

physics courses at MIT, so she decided to major in 

geophysics. 

After graduation, Atwater held an internship at Woods 

Hole Oceanographic Institute in Massachusetts. 

There, she combined the adventures of ocean sailing 

with geophysics. 

A close look in a tiny submarine 

In 1967, Atwater began graduate school at the Scripps 

Oceanographic Institution in La Jolla, California. 

During this time, many exciting geological discoveries 

were being made. The concept of sea floor spreading 

was emerging, leading to the current theory of plate 

tectonics. 

3.3 

While at Scripps, Atwater joined a research group that 

used sophisticated equipment on ships to study the sea 

floor near California. 

Part of Atwater’s later research on sea floor spreading 

involved twelve trips down to the ocean floor in the 

tiny submarine Alvin. Only Atwater and two other 

people could fit in it. Using mechanical arms, they 

collected samples on the ocean floor nearly two miles 

underwater! Atwater’s firsthand view through Alvin’s 

portholes gave her a better understanding of the 

pictures and sonar records she had studied. 

She was also amazed to see hot springs gushing out of 

the ocean floor near volcanoes. She adds, “A whole 

bunch of brand new kinds of animals were living 

there. We saw giant white tubes with bright red worms 

living in them, giant clams, octopuses, crabs, giant 

anemones, and lots of slimy things. Weird!” 

Propagating rifts 

In the 1980s, Atwater was part of a team that 

researched propagating rifts near the Galapagos 

Islands off the coast of Ecuador. Propagating rifts are 

created when sea floor spreading centers realign 

themselves in response to changes in plate motion or 

uneven magma supplies. 

Atwater also discovered many propagating rifts on the 

sea floor in the northeast Pacific Ocean and in ancient 

sea floor records worldwide. 

An Earth educator 

Atwater has been a professor at the University of 

California, Santa Barbara for over 25 years. She has 

received many awards for her work in geophysics. She 

currently studies the plate tectonic history of western 

North America. This includes how the San Andreas 

Fault and Rocky Mountains were formed. 

Atwater also works with media, museums, and 

teachers and she creates educational animations to 

educate people about Earth. She explains, “My job as 

a geoscience educator is to help as many students as 

possible to know and understand and respect our 

planet—to help them really care about it and act on 

their caring.”

Page 2 of 2 

Reading reflection 

1. How did Atwater’s family contribute to her passion for planet Earth? 

2. Why was it an exciting time to study geology while Atwater was in graduate school? 

3. Describe how Atwater has gotten close-up views of the ocean floor. 

4. What are propagating rifts and where has Atwater observed them? 

5. How does Atwater educate people about Earth? 

6. Research: The Woods Hole Oceanographic Institution—Marine Operations has used the submarine Alvin 

for many research endeavors for over 40 years. Describe some of Alvin’s noteworthy trips. 

3.3

Name: Date: 

4.1 Solving Equations with One Variable 

It is useful to know formulas for calculating different quantities. Often, the formulas are very straightforward. It’s 

easy to calculate the volume of a rectangular solid when you know the formula: 

Volume = V = length × width × height (V = l × w × h) 

and the length, width, and height of the solid. It’s a little more challenging when you know the volume, length, 

and width, but need to find the height. It then becomes necessary to solve an equation in order to determine the 

unknown (in this case, the height). 

1. The volume of a rectangular solid, with a length of 1.5 cm, is 10.98 cm 3 . The width of the same solid is 

1.2 cm. Find its height. 

Explanation/Answer: use the formula V = l × w × h, and then plug in what is known, leaving the variable 

(h) for the unknown. Solve the equation for h to find the height. 

The Work: What’s happening: 

V = l × w × h Formula 

10.98 cm 3 = 1.5 cm × 1.2 cm × h Plug in known values. 

10.98 cm 3 = 1.8 cm 2 × h Complete arithmetic, multiply 1.5 × 1.2 

Check the Work: 

Divide both sides by 1.8 cm 2 , to get h alone. 

6.1 cm = 1 × h Do the division; 10.98 cm 3 ÷ 1.8 cm 2 = 6.1 cm, 

6.1 cm = h 

V = l × w × h 

1.8 cm 2 ÷ 1.8 cm 2 = 1 

V = 1.5 cm × 1.2 cm × 6.1 cm Multiply 1.5 cm × 1.2 cm × 6.1 cm. 

If the answer is 10.98 cm 3 , the solution, h = 6.1 cm, is correct. 

1.5 cm × 1.2 cm × 6.1 cm = 10.98 cm 3 The product does equal 10.98 cm 3 , the solution is correct. 

In summary: 

10.98 cm 3 

1.8 cm 2 

------------------------ 

1.8 cm 2 

× h 

1.8 cm 2 

= 

--------------------------- 

The height (h) of a rectangular solid whose volume is 10.98 cm 3 , whose length is 1.5 cm, and whose width is 1.2 

cm, is 6.1 cm. 

4.1

Page 2 of 4 

2. The density of titanium is 4.5 g/cm3 . A titanium pendant’s mass is 2.25 grams. Use the formula 

Density = ----------------mass 

, or D = 

m 

--- , or to find its volume. 

volume v 


4.5 g × V = (2.25 g) × (1 cm 3 ) 

Formula 

Plug in known values. 

Rewrite 4.5 g/cm 3 as 

Think of 4.5 g 

1 cm 

as a proportion. 

Then set the cross products equal 

3 

------------- = 

2.25 g 

-------------- 

V 

4.5 g × V = 2.25 g × 1 cm 3 Do arithmetic: 2.25 g × 1cm 3 = 2.25 g × 1 cm 3 

Check the Work: 

In summary: 

D 

= 

m 

--v 

3 

4.5 g/cm = 

2.25 

-------------g 

V 

4.5g 

1 cm 3 

------------- 

= 

2.25 

-------------g 

V 

4.5 

--------------------g 

× V 2.25 g 1cm 

4.5 g 

3 

= ---------------------------------- 

× 

4.5 g 

Divide both sides of the equation by 4.5 g to get V alone. 

V = 0.5 cm 3 Do the division on each side. Remember to cancel units as well as 

divide the numbers. 

D 

= 

m 

--v 

3 

4.5 g/cm 

2.25 g 

0.5 cm 3 

= 

------------------ 

Divide 2.25 ÷ 0.5. If the answer is 4.5 g/cm 3 , the solution, 

V = 0.5 cm 3 , is correct. 

2.25 ÷ 0.5 = 4.5 g/cm 3 The quotient does equal 4.5 g/cm 3 ; therefore, the solution is 

correct. 

The volume of a titanium pendant whose mass is 2.25 grams is 4.5 g/cm 3 . 

4.5 g 

1 cm 3 

------------- 

4.1

Page 3 of 4 

Use the formula V = l × w × h to set up and solve for the unknown in each. 

1. Find the width (w) of a rectangular solid whose length is 12 mm, and whose height is 15 mm, if the volume 

of the solid is 720 mm 3 . 

2. Find the length of this rectangular solid whose volume is 0.12 m 3 . 

3. The length and width of a rectangular solid are 2.15 cm. Its volume is 36.98 cm 3 . Find the height of this 

rectangular solid. 

Use the formula Speed = 

distance 

-------------------- , or S = 

d 

-- to set up and solve for the unknown in each. 

time t 

Here, speed is measured in meters/second (m/s), distance is measured in meters (m), and time is measured 

in seconds (s). 

0.25 m 

0.6 m 

4. How far will a marble rolling at a speed of 0.25 m/s travel in 30. seconds? 

5. Nate throws a paper wad to Ali who is sitting exactly 1.8 meters away. The paper wad was only in the air for 

0.45 seconds. How fast was it traveling? 

6. How long does it take a battery operated toy car to travel 3 meters at a speed of 0.1 m/s? 

7. A dog is running 3.20 m/s. How long will it take him to go 100. meters? 

mass m 

Use the formula Density = ----------------- , or D = 

--- , to set up and solve for the unknown in each. 

volume v 

Here, density (D) is measured in grams per cubic centimeter (g/cm3), mass (m) is measured in grams (g), 

and volume (V) is measured in cubic centimeters (cm3). 

8. What is the density of a steel nail whose volume is 3.2 cm 3 and whose mass is 25 g? 

9. Find the mass of a cork whose density is 0.12 g/cm 3 and whose volume is 9.0 cm 3 ? 

10. An ice cube’s volume is 4.9 cm 3 . Find its mass if its density is 0.92 g/cm 3 . 

11. A solid plastic ball’s mass is 225 g. The density of the plastic is 2.00 g/cm 3 . What is the volume of the ball? 

12. Find the volume of an ice cube whose mass is 2.08 g. See question #10 for the density of ice. 

Use the formula: Force = pressure × area to set up and solve for each unknown. 

? 

4.1

Page 4 of 4 

Here, force is measured in Newtons (N), pressure is measured in Pascals (Pa), and area is 

measured in square meters (m2). Hint: 1 Pa = 1 N / m 2 . 

• A drinking glass is sitting on the kitchen table. The glass has a weight of 2 N. Its base has an area of 

0.005 m2 . How much pressure does the drinking glass exert on the table? 

Explanation/Answer: 


Force = pressure × area Formula 

2 N = p × 0.005m 2 Plug in known values. 

2 N 

0.005 m 2 

--------------------- 

In summary: 

× 

0.005 m 2 

= 

------------------------------ 

p 0.005 m 2 

400 N/m 2 = p × 1 

Divide both sides by 0.005 m 2 to get p alone. 

Do the division: 

2 N ÷ 0.005 m2 = 400 N / m2 , 0.005 m2 ÷ 0.005 m2 = 1 

400 Pa = p Rewrite 400 N/m 2 as 400 Pa, multiply; p × 1 = p. 

A drinking glass with a weight of 2 N and whose base has area 0.005 m 2 exerts 400 Pa of pressure on the table 

it sits on. 

1. A tea kettle’s base has an area of 0.008 m 2 . It is puts 1,000 Pascals of pressure on the stove where it sits. 

What is the weight of the kettle? 

2. A block of wood whose base has an area of 4 m 2 has a weight of 80 N. How much pressure does the block 

place on the floor on which it sits? 

3. A sculpture’s base has an area of 2.50 m 2 . How much pressure does the sculpture place on the wooden 

display case where it sits, if it has a weight of 540. N? 

4. A student is breaking class rules by standing on a chair. If her feet have a total area of 0.04 m 2 , and her 

weight is 600. N, how much pressure is she putting on the chair? 

4.1

Name: Date: 

4.1 Problem Solving Boxes 

Looking for Solution 

Given 

Relationships 


Given 

Relationships 


Given 

Relationships 

4.1

Name: Date: 

4.1 Problem Solving with Rates 

Solving mathematical problems often involves using rates. An upside down rate is called a reciprocal rate. 

A rate may be written as its reciprocal because no matter how you write it the rate gives you the same amount of 

one thing per amount of the other thing. For example, you can write 5 cookies/ $1.00 or $1.00/5 cookies. For 

$1.00, you know you will get 5 cookies no matter how you write the rate. In this activity, you will choose how to 

write each rate in order to solve the problem the easiest way. 

Steps for solving problems with rates are listed below. Remember, after you have set up your problem, analyze 

and cancel the units by crossing them out, then do the arithmetic, and provide the answer. Remember that the 

answer always consists of a number and a unit. 

In the space provided, write the reciprocal rate of each given rate. The first one is done for you. 

1. 

2. 

3. 

4. 

5. 

Step 1 What quantity or rate are you asked for in the problem? Write it down. 

Step 2 What do you know from reading the problem? List all known rates and quantities. 

Step 3 Arrange the known quantities and rates to get an answer that has the right units. This arrangement 

might include a formula. 

Step 4 Plug in the values you know. 

Step 5 Solve the problem and write the answer with a number and a unit. 

-------------------- 

1 year 

365 days 

= 

---------------------- 

12 inches 

= 

foot 

3 

--------------------------------small 

pizzas 

= 

$10.00 

36 

----------------------pencils 

= 

3 boxes 

365 

-------------------days 

1 year 

18 

---------------------------------------------------gallons 

of gasoline 

= 

360 miles 

4.1

Page 2 of 3 

In problems 6 and 7, you will be shown how to set up steps 1–4. For step 5, you will need to solve 

the problem and write the answer as a number and unit. 

6. Downhill skiing burns about 600. calories per hour. How many calories will you burn if you 

downhill ski for 3.5 hours? 

Step 1 Looking for calories. 

Step 2 600. calories/hour; 3.5 hours 

Step 3 

Step 4 

Step 5 Answer: 

7. How many cans of soda will John drink in a year if he drinks 3 sodas per day? (Remember that there are 365 

days in a year.) 

Step 1 Looking for cans of soda per year. 

Step 2 3 sodas/day; 365 days/year 

Step 3 

Step 4 


8. How many heartbeats will a person have in a week if he has an average heart rate of 72 beats per minute? 

(Remember the days/week, hours/day, and minutes/hour. 

Step 1 Looking for number of heartbeats per week. 

Step 2 72 heartbeats/minute, 7 days/week, 24 hours/day, 60 minutes/hour 

Step 3 

Step 4 


calories 

----------------- × hours = calorie 

hour 

600 

----------------------------calories 

× 3.5 hours = calories 

hour 

soda 

--------day 

days 

× ---------- = 

year 

sodas 

-----------year 

3 sodas 365 days 

----------------- × --------------------day 

year 

= 

sodas 

-----------year 

heartbeats 

----------------------minute 

minutes 

-----------------hours 

× ------------days 

× × ----------hour 

day week 

--------------------------------- 

72 heartbeats 

minute 

60 minutes 

× -------------------------hour 

= 

24 hours 

× -------------------day 

heartbeats 

----------------------week 

7 days 

× --------------week 

= 

heartbeats 

----------------------week 

4.1

Page 3 of 3 

Using the five problem-solving steps, solve the following problems on your own. Be sure to read 

the problem carefully. Show your work in the blank provided. 

Step 1 What quantity or rate are you asked for in the problem? Write it down. 

Step 2 What do you know from reading the problem? List all known rates and quantities. 

Step 3 Arrange the known quantities and rates to get an answer that has the right units. This 

arrangement might include a formula. 

Step 4 Plug in the values you know. 

Step 5 Solve the problem and write the answer with a number and a unit. 

9. How much will you pay for 5 pounds of shrimp if the cost is 2 pounds for $10.99? 

10. How many miles can you get on one tank of gas if your tank holds 18 gallons and you get 23 miles per 

gallon? 

11. What is your rate in miles/hour if you run at a speed of 2.2 miles in 20. minutes? 

12. Suppose for your cookout you need to make 100 hamburgers. You know that 2.00 pounds will make 

9 hamburgers. How many pounds will you need? 

13. What is your mass in kilograms if you weigh 120. pounds? (There are approximately 2.2 pounds in one 

kilogram.) 

14. Mt. Everest is 29,028 feet high. How many miles is this? (There are exactly 5,280 feet in one mile.) 

15. Susan works 8 hours a day and makes $7.00 per hour. How much money does Susan earn in one week if she 

works 5 days per week? 

16. How many years will it take a major hamburger fast food chain to sell 45,000,000 burgers if it sells 

approximately 12,350 burgers per day? 

17. Your science teacher needs to make more of a salt-water mixture. The concentration of the mixture that is 

needed is 35 grams of salt in 1,000. milliliters of water. How many grams of salt will be needed to make 

1,500. milliliters of the salt-water? 

18. A cart travels down a ramp at an average speed of 5.00 centimeters/second. What is the speed of the cart in 

miles/hour? (Remember there are 100 centimeters per meter, 1000 meters/kilometer, and 1.6 kilometer per 

mile.) 

19. A person goes to the doctor and will need a 3-month prescription of medicine. The person will be required to 

take 3 pills per day. How many pills will the doctor write the prescription for assuming there are 30 days in a 

month? 

20. If you are traveling at 65 miles per hour, how many feet will you be traveling in one second? 

4.1

Name: Date: 

4.1 Percent Error 

When you do scientific experiments that involve measurements, your results may fit the trend that is 

expected. However, it is unlikely that the numbers will turn out exactly as expected. 

In an experiment, you often make a prediction about an event’s outcome, but find that your actual measured 

outcome is slightly different. The percent error (% Error) gives you a means to evaluate how far apart your 

prediction and measured values are. 

Percent error is calculated as the absolute value of the difference between the predicted and measured values 

divided by the true value multiplied by 100, or: 

measured value – predicted value 

% Error = 

---------------------------------------------------------------------------------- × 100 

true value 

Which value is the true value? That depends on your experiment design. If you want to evaluate how well a graph 

is able to predict an actual event (like how far a marble will travel or how long a car will take to travel down a 

ramp) then you use the measured value as the true value. 

On the other hand, if you have carefully calculated how much product you should get in a chemical reaction, and 

you want to evaluate how carefully you made your measurements and followed the procedure, then you would 

use the predicted value as the true value. 

Remember that with percent error, smaller is better. A perfect outcome would have zero percent error. 

Some students are conducting an experiment using a toy car with a track, timer, and photogates. 

Their task is to determine how quickly the car will travel a given distance, and then to predict and test the last trip 

that the car takes. The table below shows the distances and times traveled by the car so far. 

Distance from A to B 

(cm) 

Time from A to B (sec) 

10. 0.3305 

20. 0.3380 

40. 0.3535 

50. 0.3610 

60. ? 

Based on an estimation made by extending their graph, the students predict that it will take the car 0.3685 

seconds to travel 60 centimeters. When the experiment was conducted three times, it took the car 0.3669, 0.3680, 

and 0.3694 seconds to make the trip. Calculate the percent of error based on the predicted and actual outcomes. 

4.1

Page 2 of 3 

Solution: 

The process: 

1. Average the times recorded in the three 60-centimeter trials to use as the measured value in the formula. 

2. Calculate percent error using the formula given above, using the average from (1) as the measured value. 

The work: 

1. Find the average: 

2. Calculate: 

0.3669 

---------------------------------------------------------- 

+ 0.368 + 0.3694 

= 

1.1043 

--------------- = 0.3681 

3 

3 

% Error 

measured value – predicted value 

= ------------------------------------------------------------------------------- × 100 

true value 

0.3681 – 0.3685 

% Error -------------------------------------- 

0.0004 

= × 100 = --------------- × 100 ≈ 

0.11% 

0.3681 

0.3981 

The Answer: The percent error in this particular experiment is 0.11%. This means that the student’s predicted 

time was 0.11% off the actual, measured time. 

Use the method shown in the example to calculate the percent error in each of the following problems. 

Part I: This table was constructed by a group of students conducting an experiment similar to the one in the 

example above, but using a different incline. Complete the table using the average time calculated at each 

distance from the information provided in the problems below. 


(cm) 

Time from A to B (sec) 

10. 1.0050 

20. 1.8877 

30. 2.8000 

40. 3.7850 

50. ? 

60. ? 

70. ? 

80. ? 

90. ? 

4.1

Page 3 of 3 

1. The lab group conducting this experiment decided to call themselves “the Science Sleuths.” They 

graphed the data shown in the table and based on their graph, predicted that it would take the car 

4.7500 seconds to travel 50 centimeters. The three trials they conducted resulted in 4.8020, 4.8100, 

and 4.7000 seconds. What is the percent error? Remember to update the table. 

2. The Sleuths predict that the car will travel 60 centimeters in 5.7950 seconds. Their trials gave times of 

5.7702, 5.8000, and 5.2600 seconds. What is the percent error here? 

3. For 70 centimeters, the trial runs resulted in 6.9150, 6.8080, and 7.0003 seconds. The Sleuths had predicted 

that it would take the car 6.8150 seconds to cover the distance. Calculate the percent error. 

4. The Sleuths’ car took 7.9903, 7.9995, and 7.9047 seconds to travel 80 centimeters. They had predicted a 

time of 7.9520 seconds. What is the percent error? 

5. This time, the Sleuths predicted that it would take the car 9.0000 seconds flat to cover the 90 centimeters it 

needed to travel. It actually took the car 8.9907, 9.0006, and 9.0507 seconds in each of three trials. Find the 

percent error. 

6. Lisa was trying out for the track team at her middle school. The coach asked her to make predictions about 

how fast she could run each of the sprint events, then timed her in each event on three different days. All the 

information is shown in the table below. Calculate Lisa’s percent error for her prediction in each event. 

Event Predicted time (s) Actual times (s) 

17.55 

100 m 18.05 

18.94 

15.06 

41.05 

200 m 34.70 

38.22 

35.90 

72.75 

400 m 67.45 

65.10 

65.88 

Calculate the percent error for each event: 

a. 100 m 

b. 200 m 

c. 400 m 

4.1

Name: Date: 

4.1 Speed 

To determine the speed of an object, you need to know the distance traveled and the time taken to travel that 

distance. If you know the speed, you can determine the distance traveled or the time it took—you just rearrange 

the formula for speed, v = d/t. For example, 

Equation... Gives you... If you know... 

v = d/t speed distance and time 

d = v × t distance speed and time 

t = d/v time distance and speed 

Use the SI system to solve the practice problems unless you are asked to write the answer using the English 

system of measurement. As you solve the problems, include all units and cancel appropriately. 

Example 1: What is the speed of a cheetah that travels 112.0 meters in 4.0 seconds? 

Looking for 

Given 

Speed of the cheetah. 

Distance = 112.0 meters 

Time = 4.0 seconds 

Relationship 

Solution 

The speed of the cheetah is 28 meters per second. 

Example 2: There are 1,609 meters in one mile. What is this cheetah’s speed in miles/hour? 

Looking for 

Given 

Speed of the cheetah in miles per hour. 

Speed = 28 m/s (from solution to Example 1) 

Relationships 

speed 

= 

speed = 

d 

-- 

t 

and 1, 609 meters = 1 mile 

d 

-- 

t 

Solution 

speed 

28 

----------m 

s 

× 

= 

d 

-- = 

112.0 

-----------------m 

= 

t 4.0 s 

------------------ 

1 mile 

1,609 m 

3, 600 s 

× ----------------- 

1 hour 

28 

----------m 

s 

63 

------------------miles 

hour 

The speed of the cheetah in miles per hour is 

63 mph. 

= 

4.1

Page 2 of 3 

1. A bicyclist travels 60.0 kilometers in 3.5 hours. What is the cyclist’s average speed? 


Given 

Relationships 

2. What is the average speed of a car that traveled 300.0 miles in 5.5 hours? 

3. How much time would it take for the sound of thunder to travel 1,500 meters if sound travels at a speed of 

330 m/s? 

4. How much time would it take for an airplane to reach its destination if it traveled at an average speed of 

790 kilometers/hour for a distance of 4,700 kilometers? What is the airplane’s speed in miles/ hour? 

5. How far can a person run in 15 minutes if he or she runs at an average speed of 16 km/hr? 

(HINT: Remember to convert minutes to hours.) 

6. In problem 5, what is the runner’s distance traveled in miles? 

7. A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in 

15 minutes? 

8. You know that there are 1,609 meters in a mile. The number of feet in a mile is 5,280. Use these equalities to 

answer the following problems: 

a. How many centimeters equals one inch? 

b. What is the speed of the snail in problem 7 in inches per minute? 

9. Calculate the average speed (in km/h) of a car stuck in traffic that drives 12 kilometers in 2 hours. 

10. How long would it take you to swim across a lake that is 900 meters across if you swim at 1.5 m/s? 

a. What is the answer in seconds? 

b. What is the answer in minutes? 

11. How far will a you travel if you run for 10. minutes at 2.0 m/s? 

12. You have trained all year for a marathon. In your first attempt to run a marathon, you decide that you want to 

complete this 26.2-mile race in 4.5 hours. 

a. What is the length of a marathon in kilometers (1 mile = 1.6 kilometers)? 

b. What would your average speed have to be to complete the race in 4.5 hours? Give your answer in 

kilometers per hour. 

4.1

Page 3 of 3 

13. Suppose you are walking home after school. The distance from school to your home is five 

kilometers. On foot, you can get home in 25 minutes. However, if you rode a bicycle, you could get 

home in 10 minutes. 

a. What is your average speed while walking? 

b. What is your average speed while bicycling? 

c. How much faster you travel on your bicycle? 

14. Suppose you ride your bicycle to the library traveling at 0.50 km/min. It takes you 25 minutes to get to the 

library. How far did you travel? 

15. You ride your bike for a distance of 30 km. You travel at a speed of 0.75 km/ minute. How many minutes 

does this take? 

16. A train travels 225 kilometers in 2.5 hours. What is the train’s average speed? 

17. An airplane travels 3,280 kilometers in 4.0 hours. What is the airplane’s average speed? 

18. A person in a kayak paddles down river at an average speed of 10. km/h. After 3.25 hours, how far has she 

traveled? 

19. The same person in question 18 paddles upstream at an average speed of 4 km/h. How long would it take her 

to get back to her starting point? 

20. An airplane travels from St. Louis, Missouri to Portland, Oregon in 4.33 hours. If the distance traveled is 

2,742 kilometers, what is the airplane’s average speed? 

21. The airplane returns to St. Louis by the same route. Because the prevailing winds push the airplane along, 

the return trip takes only 3.75 hours. What is the average speed for this trip? 

22. The airplane refuels in St. Louis and continues on to Boston. It travels at an average speed of 610 km/h. If 

the trip takes 2.75 hours, what is the flight distance between St. Louis and Boston? 

Challenge Problems: 

23. The speed of light is about 3.00 × 10 5 km/s. It takes approximately 1.28 seconds for light reflected from the 

moon to reach Earth. What is the average distance from Earth to the moon? 

24. The average distance from the sun to Pluto is approximately 6.10 × 10 9 km. How long does it take light from 

the sun to reach Pluto? Use the speed of light from the previous question to help you. 

25. Now, make up three speed problems of your own. Give the problems to a friend to solve and check their 

work. 

a. Make up a problem that involves solving for average speed. 

b. Make up a problem that involves solving for distance. 

c. Make up a problem that involves solving for time. 

4.1

Name: Date: 

4.1 Velocity 

Speed and velocity do not have the same meaning to scientists. Speed is a scalar quantity, which means it can be 

completely described by its magnitude (or size). The magnitude is given by a number and a unit. For example, an 

object’s speed may be measured as 15 meters per second. 

Velocity is a vector quantity. In order to measure a vector quantity, you must know the both its magnitude and 

direction. The velocity of an object is determined by measuring both the speed and direction in which an object is 

traveling. 

• If the speed of an object changes, then its velocity also changes. 

• If the direction in which an object is traveling changes, then its velocity changes. 

• A change in either speed, direction, or both causes a change in velocity. 

You can rearrange v = d/t to solve velocity problems the same way you solved speed problems earlier in this 

course. The boldfaced v is used to represent velocity as a vector quantity. The variables d and t are used for 

distance and time. The velocity of an object in motion is equal to the distance it travels per unit of time in a 

given direction. 

Example 1: What is the velocity of a car that travels 100.0 meters, northeast in 4.65 seconds? 

Looking for 

Velocity of the car. 

Given 

Distance = 100.0 meters 


Relationship 

Solution 

The velocity of the car is 21.5 meters per second, 

northeast. 

Example 2: A boat travels with a velocity equal to 14.0 meters per second, east in 5.15 seconds. What distance 

in meters does the boat travel? 

Looking for 

Given 

velocity 

Distance the boat travels. 

Velocity = 14.0 meters per second, east 


Relationship 

= 

d 

-- 

t 

distance = 

v × t 

Solution 

velocity 

distance = v× t = 

= 

d 

-- = 

100.0 

-----------------m 

= 

t 4.65 s 

The boat travels 72.1 meters. 

21.5 

--------------m 

s 

14.0 

--------------m 

× 5.15 s= 

72.1 m 

s 

4.1

Page 2 of 2 

1. An airplane flies 525 kilometers north in 1.25 hours. What is the airplane’s velocity? 


Given 

Relationship 

2. A soccer player kicks a ball 6.5 meters. How much time is needed for the ball to travel this distance if its 

velocity is 22 meters per second, south? 

3. A cruise ship travels east across a river at 19.0 meters per minute. If the river is 4,250 meters wide, how long 

does it take for the ship to reach the other side? 

4. Joaquin mows the lawn at his grandmother’s home during the summer months. Joaquin measured the 

distance across his grandmother’s lawn as 11.5 meters. 

a. If Joaquin mows one length across the lawn from east to west in 7.10 seconds, then what is the velocity 

of the lawnmower? 

b. Once he reaches the edge of the lawn, Joaquin turns the lawnmower around. He mows in the opposite 

direction but maintains the same speed. What is the velocity of the lawnmower? 

5. A family drives 881 miles from Houston, Texas to Santa Fe, New Mexico for vacation. How long will it take 

the family to reach their destination if they travel at a velocity of 55.0 miles per hour, northwest? 

6. A shopping cart is pushed 15.6 meters west across a parking lot in 5.2 seconds. What is the velocity of the 

shopping cart? 

7. Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it 

travels 9.5 meters south in 2.1 seconds. 

a. What is the velocity of the tennis ball? 

b. If the tennis ball travels at constant speed, what is its velocity when Liam returns Katie’s serve? 

8. A driver realizes that she is traveling in the wrong direction on a one-way street. She has already driven 

350 meters at a velocity of 16 meters per second, east before deciding to make a U-turn. How long did it take 

for the driver to realize her error? 

9. Juan’s mother drives 7.25 miles southwest to her favorite shopping mall. What is the average velocity of her 

automobile if she arrives at the mall in 20. minutes? 

10. A bus is traveling at 79.7 kilometers per hour east. How far does the bus travel 1.45 hours? 

11. A girl scout troop hiked 5.8 kilometers southeast in 1.5 hours.What was the troop’s velocity? 

12. A volcanologist noted that a lahar rushed down a mountain at 32.2 kilometers per hour, south. How far did 

the mud flow in 17.5 minutes? 

4.1

Name: Date: 

4.2 Calculating Slope from a Graph 

To determine the slope of a line in a graph, first choose two points on the line. Then count how many steps up or 

down you must move to be on the same horizontal line as your second point. Multiply this number by the scale of 

your horizontal axis. For example, if your x-axis has a scale of 1 box = 20 cm, then multiply the number of boxes 

you counted by 20 cm. 

Put the result along with the positive or negative sign as the top (numerator) of your slope ratio. Then count how 

many steps you must move right or left to land on your second point. Multiply the number of steps by the scale of 

your vertical axis. Place the results as the bottom (denominator) of your slope ratio. Then reduce the fraction of 

your ratio. This number is the slope of the line. Note: The letter m is used to represent slope in an equation. 

A The chosen points for Example A are (0, 0) and (3, 9). There are many 

choices for this graph, but only one slope. If you have the point (0, 0), 

you should choose it as one of your points. 

It takes 9 vertical steps to move from (0, 0) to (0, 9). Put a 9 in the 

numerator of your slope ratio (or subtract 9 – 0). Then count the 

number of steps to move from (0, 9) to (3, 9). This is your denominator 

of your slope ratio. Again, you can do this by subtraction (3 – 0). 

m = 

9 

3 

= 

3 

1 

B The two points that have been chosen for Example B are (0, 24) and 

(6, 15). Be careful of the scales on each of the axes. 

It takes 3 vertical steps to go from (0, 24) to (0, 15). But each of these 

steps has a scale of 3. So you put a –9 into the numerator of the slope 

ratio. It is negative because you are moving down from one point to the 

other. Then count the steps over to (6, 15). There are 3 steps but each 

counts for 2 so you put a 6 into the denominator of the slope ratio. 

m = 

−9 6 

= 

−3 

2 

Find the slope of the line in each of the following graphs: 

Graph #1: Graph #2: 

4.2

Page 2 of 2 





4.2

Name: Date: 

4.2 Analyzing Graphs of Motion With Numbers 

Speed can be calculated from position-time graphs and distance can be calculated from speed-time graphs. Both 

calculations rely on the familiar speed equation: v = d/t. 

This graph shows position and time for a sailboat starting from its 

home port as it sailed to a distant island. By studying the line, you can 

see that the sailboat traveled 10 miles in 2 hours. 

• Calculating speed from a position-time graph 

The speed equation allows us to calculate that the boat’s speed during 

this time was 5 miles per hour. 

v = d/t 

v = 10 miles ⁄ 2 hours 

v = 

5 miles/hour, read as 5 miles per hour 

This result can now be transferred to a speed-time graph. Remember 

that this speed was measured during the first two hours. 

The line showing the boat’s speed is horizontal because the speed was 

constant during the two-hour period. 

• Calculating distance from a speed-time graph 

Here is the speed-time graph of the same sailboat later in the voyage. 

Between the second and third hours, the wind freshened and the 

sailboat gradually increased its speed to 7 miles per hour. The speed 

remained 7 miles per hour to the end of the voyage. 

How far did the sailboat go during the six-hour trip? We will first 

calculate the distance traveled during the fourth, fifth, and sixth hours. 

4.2

Page 2 of 4 

On a speed-time graph, distance is equal to the area between the baseline and the plotted line. You know 

that the area of a rectangle is found with the equation: A = L × W. Similarly, multiplying the speed from 

the y-axis by the time on the x-axis produces distance. Notice how the labels cancel to produce miles: 

speed × time = distance 

Now that we have seen how distance is calculated, we can consider the distance 

covered between hours 2 and 3. 

The easiest way to visualize this problem is to think in geometric terms. Find the 

area of the triangle (Area A), then find the area of the rectangle (Area B), and add 

the two areas. 

Area of triangle A 

Geometry formula 

Area of rectangle B 

Geometry formula 

Add the two areas 

7 miles/hour × ( 6 hours – 3 hours) 

= distance 

7 miles/hour × 3 hours = distance = 21 miles 

The area of a triangle is one-half the area of a rectangle. 

time 

speed × --------- = distance 

2 

( 7 miles/hour – 5 miles/hour) 

speed × time = distance 

The Position vs. Time graph on page 1 tells us that the boat traveled 

10 miles in the first two hours. According to our calculations, the boat 

traveled 6 miles during the third hour and 21 miles in hours four through 

six. 

Therefore the total distance traveled is 10 + 6 + 21 = 37 miles. 

We can now use this information about distance to complete our positiontime 

graph: 

( 3 hours – 2 hours) 

× ---------------------------------------------- = distance = 1 mile 

2 

5 miles/hour × ( 3 hours – 2 hours) 

= distance = 5 miles 

Area A + Area B = distance 

1 miles+ 5 mile = distance = 

6 miles 

4.2

Page 3 of 4 

1. For each position-time graph, calculate and plot speed on the speed-time graph to the right. 

a. The bicycle trip through hilly country 

a. A walk in the park 

b. Strolling up and down the supermarket aisles 

4.2

Page 4 of 4 

2. For each speed-time graph, calculate and plot the distance on the position-time graph to the right. 

For this practice, assume that movement is always away from the starting position. 

a. The honey bee among the flowers 

b. Rover runs the street 

c. The amoeba 

4.2

Name: Date: 

4.2 Analyzing Graphs of Motion Without Numbers 

Position-time graphs 

The graph at right represents the story of “The Three Little Pigs.” The 

parts of the story are listed below. 

• The wolf started from his house. The graph starts at the origin. 

• Traveled to the straw house. The line moves upward. 

• Stayed to blow it down and eat dinner. The line is flat because position 

is not changing. 

• Traveled to the stick house. The line moves upward again. 

• Again stayed, blew it down, and ate seconds. The line is flat. 

• Traveled to the brick house. The line moves upward. 

• Died in the stew pot at the brick house. The line is flat. 

The graph illustrates that the pigs’ houses are generally in a line away from the wolf’s house and that the brick 

house was the farthest away. 

Speed-time graphs 

A speed-time graph displays the speed of an object over time and is based on 

position-time data. Speed is the relationship between distance (position) and 

time, v = d/t. For the first part of the wolf’s trip in the position versus time 

graph, the line rises steadily. This means the speed for this first leg is constant. 

If the wolf traveled this first leg faster, the slope of the line would be steeper. 

The wolf moved at the same speed toward his first two “visits.” His third trip 

was slightly slower. Except for this slight difference, the wolf was either at one 

speed or stopped (shown by a flat line in the speed versus time graph). 

Read the steps for each story. Sketch a position-time graph and a speed-time graph for each story. 

1. Graph Red Riding Hood’s movements 

according to the following events listed in 

the order they occurred: 

• Little Red Riding Hood set out for 

Grandmother’s cottage at a good walking pace. 

• She stopped briefly to talk to the wolf. 

• She walked a bit slower because they were 

talking as they walked to the wild flowers. 

• She stopped to pick flowers for quite a 

while. 

• Realizing she was late, Red Riding Hood ran the rest of the way to Grandmother’s cottage. 

4.2

Page 2 of 2 

2. Graph the movements of the Tortoise and the Hare. Use two lines to show the movements of each 

animal on each graph. The movements of each animal is listed in the order they occurred. 

• The tortoise and the hare began 

their race from the combined 

start-finish line. By the end of 

the race, the two will be at the 

same position at which they 

started. 

• Quickly outdistancing the 

tortoise, the hare ran off at a 

moderate speed. 

• The tortoise took off at a slow 

but steady speed. 

• The hare, with an enormous lead, stopped for a short nap. 

• With a startle, the hare awoke and realized that he had been sleeping for a long time. 

• The hare raced off toward the finish at top speed. 

• Before the hare could catch up, the tortoise’s steady pace won the race with an hour to spare. 

3. Graph the altitude of the sky rocket on its flight according to the following sequence of events listed in order. 

• The sky rocket was placed on the 

launcher. 

• As the rocket motor burned, the rocket 

flew faster and faster into the sky. 

• The motor burned out; although the 

rocket began to slow, it continued to 

coast even higher. 

• Eventually, the rocket stopped for a split 

second before it began to fall back to 

Earth. 

• Gravity pulled the rocket faster and faster toward Earth until a parachute popped out, slowing its 

descent. 

• The descent ended as the rocket landed gently on the ground. 

4. A story told from a graph: Tim, a student at Cumberland School, was determined to ask Caroline for a movie 

date. Use these graphs of his movements from his house to Caroline’s to write the story. 

4.2

Name: Date: 

4.3 Acceleration 

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the 

formula below. The units for acceleration are meters per second per second or m/s 2 . 

A positive value for acceleration shows speeding up, and negative value for acceleration shows slowing down. 

Slowing down is also called deceleration. 

The acceleration formula can be rearranged to solve for other variables such as final speed (v2) and time (t). 

v2 = v1 + ( a× t) 

t = 

v2 – v1 --------------a 

1. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? 

Looking for 

Acceleration of the skater 

Given 

Beginning speed = 2.0 m/s 

Final speed = 10.0 m/s 

Change in time = 3.0 seconds 

Relationship 

v2 – v1 a = --------------t 

Solution 

The acceleration of the skater is 2.7 meters per 

second per second. 

2. A car accelerates at a rate of 3.0 m/s 2 . If its original speed is 8.0 m/s, how many seconds will it take the car 

to reach a final speed of 25.0 m/s? 

Looking for 

Acceleration 

The time to reach the final speed. 

Given 

Beginning speed = 8.0 m/s; Final speed = 25.0 m/s 

Acceleration = 3.0 m/s2 Relationship 

v2 – v1 t = 

--------------a 

= 

Final 

-----------------------------------------------------------------------speed 

– Beginning speed 

Time 

a = 

v2 – v1 --------------t 

Acceleration 

Solution 

Time 

10.0 

-------------------------------------------m/s 

– 2.0 m/s 

2.7 m/s 

3.0 s 

2 

= = 

25.0 m/s – 8.0 m/s 

3.0 m/s 2 

= ------------------------------------------- = 5.7 s 

The time for the car to reach its final speed is 

5.7 seconds. 

4.3

Page 2 of 2 

1. While traveling along a highway, a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the 

automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.) 

2. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 

4.5 seconds. What is the acceleration of the dragster? 

3. The table below contains data for a ball rolling down a hill. Fill in the missing data values in the table and 

determine the acceleration of the rolling ball. 

Time (seconds) Speed (km/h) 

0 (start) 0 (start) 

2 3 

6 

9 

8 

10 15 

4. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much 

time will it take for the car to stop if it decelerates at –4.0 m/s 2 ? 

5. If a car can go from 0 to 60. mph in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting 

speed were 50. mph? 

6. A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s 2 . If the cart has a beginning 

speed of 2.0 m/s, what is its final speed? 

7. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this 

helicopter? 

8. As she climbs a hill, a cyclist slows down from 25 mph to 6 mph in 10 seconds. What is her deceleration? 

9. A motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s 2 for 6.0 seconds. What is the final speed of 

the motorcycle? 

10. A car starting from rest accelerates at a rate of 8.0 m/s. What is its final speed at the end of 4.0 seconds? 

11. After traveling for 6.0 seconds, a runner reaches a speed of 10. m/s. What is the runner’s acceleration? 

12. A cyclist accelerates at a rate of 7.0 m/s 2 . How long will it take the cyclist to reach a speed of 18 m/s? 

13. A skateboarder traveling at 7.0 meters per second rolls to a stop at the top of a ramp in 3.0 seconds. What is 

the skateboarder’s acceleration? 

4.3

Name: Date: 

4.3 Acceleration and Speed-Time Graphs 

Acceleration is the rate of change in the speed of an object. The graph below shows that object A accelerated 

from rest to 10 miles per hour in two hours. The graph also shows that object B took four hours to accelerate 

from rest to the same speed. Therefore, object A accelerated twice as fast as object B. 

Calculating acceleration from a speed-time graph 

The steepness of the line in a speed-time graph is related to 

acceleration. This angle is the slope of the line and is found by 

dividing the change in the y-axis value by the change in the xaxis 

value. 

Acceleration 

Δy 

----- 

Δx 

In everyday terms, we can say that the speed of object A 

“increased 10 miles per hour in two hours.” Using the slope 

formula: 

Acceleration 

= 

Δy 

----- = -------------------------------------- 

10 mph – 0 mph 

= 

Δx 2 hours – 0 hour 

• Acceleration = Δy/Δx (the symbol Δ means “change in”) 

• Acceleration = (10 mph – 0 mph)/(2 hours – 0 hours) 

• Acceleration = 5 mph/hour (read as 5 miles per hour per hour) 

The double per time label attached to all accelerations may seem confusing at first. It is not so alien a concept if 

you break it down into its parts: 

The speed changes. . . . . . during this amount of time: 

5 miles per hour each hour 

Accelerations can be negative. If the line slopes downward, Δy will be a negative number because a larger value 

of y will be subtracted from a smaller value of y. 

Calculating distance from a speed-time graph 

= 

5 

-------------mph 

hour 

The area between the line on a speed-time graph and the baseline is equal to the distance that an object travels. 

This follows from the rate formula: 

Rate or Speed = 

Distance 

-------------------- 

Time 

v = 

d 

-- 

t 

4.3

Page 2 of 3 

Or, rewritten: 

Notice how the labels cancel to produce a new label that fits the result. 

Here is a speed-time graph of a boat starting from one place and 

sailing to another: 

The graph shows that the sailboat accelerated between the second and 

third hour. We can find the total distance by finding the area between 

the line and the baseline. The easiest way to do that is to break the 

area into sections that are easy to solve and then add them together. 

• Use the formula for the area of a rectangle, A = L × W, to find 

areas A, B, and D. 

• Use the formula for finding the area of a triangle, A = l × w/2, to find area C. 

Calculate acceleration from each of these graphs. 

1. Graph 1: 

2. Graph 2: 

A+ B + C + D = distance 

vt = d 

miles/hour × 3 hours = 3 miles 

A+ B + C + D = distance 

10 miles + 5 miles + 1 mile + 21 miles = 

37 miles 

4.3

Page 3 of 3 

3. Graph 3: 

4. Find acceleration for segment 1 and segment 2 in this graph: 

5. Calculate total distance for this graph: 



4.3

Name: Date: 

4.3 Acceleration Due to Gravity 

Acceleration due to gravity is known to be 9.8 meters/second/second or 

9.8 m/s 2 and is represented by g. Three conditions must be met before we can 

use this value: 

(1) the object must be in free fall 

(2) the object must have negligible air resistance, and 

(3) the object must be close to the surface of Earth. 

In all of the examples and problems, we will assume that these conditions have 

been met. Remember that speed refers to “how fast” in any direction, but 

velocity refers to “how fast” in a specific direction. The sign of numbers in 

these calculations is important. Velocities upward shall be positive, and 

velocities downward shall be negative. Because the y-axis of a graph is 

vertical, change in height shall be indicated by y. 

Here is the equation for solving for velocity: 

final velocity = initial velocity + ( the acceleration due to the force of gravity × time) 

v = v0+ gt 

Imagine that an object falls for one second. We know that at the end of the 

second it will be traveling at 9.8 meters/second. However, it began its fall at 

zero meters/second. Therefore, its average velocity is half of 

9.8 meters/second. We can find distance by multiplying this average velocity 

by time. 

Here is the equation for solving for distance. See if you can find these concepts in the equation: 

distance 

OR 

the acceleration due to the force of gravity × time 

= ---------------------------------------------------------------------------------------------------------------------- × time 

2 

OR 

y = 

1 

--gt 

2 

2 

4.3

Page 2 of 3 

Example 1: How fast will a pebble be traveling 3.0 seconds after being dropped? 

v = v0+ gt 

+ ( – × 3.0 s) 

v 0 9.8 m/s 2 

(Note that gt is negative because the direction is downward.) 

Example 2: A pebble dropped from a bridge strikes the water in 4.0 seconds. How high is the bridge? 

y 

y 

= 

= 

= 

v = – 29 m/s 

y 

1 

-- × 9.8 m/s × 4.0 s × 4.0 s 

2 

Note that the seconds cancel. The answer written with the correct number of significant figures is 78 meters. The 

bridge is 78 meters high. 

1. A penny dropped into a wishing well reaches the bottom in 1.50 seconds. What was the velocity at impact? 

2. A pitcher threw a baseball straight up at 35.8 meters per second. What was the ball’s velocity after 

2.50 seconds? (Note that, although the baseball is still climbing, gravity is accelerating it downward.) 

3. In a bizarre but harmless accident, a watermelon fell from the top of the Eiffel Tower. How fast was the 

watermelon traveling when it hit the ground 7.80 seconds after falling? 

4. A water balloon was dropped from a high window and struck its target 1.1 seconds later. If the balloon left 

the person’s hand at –5.0 meters per second, what was its velocity on impact? 

5. A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the mine 

shaft? 

6. A boy threw a small bundle toward his girlfriend on a balcony 10. meters above him. The bundle stopped 

rising in 1.5 seconds. How high did the bundle travel? Was that high enough for her to catch it? 

= 

1 

--gt 

2 

2 

1 

-- 9.8 m/s 

2 

2 

× × 4.0 s × 4.0 s 

y = 

78.4 meters 

The equations demonstrated so far can be used to find time of flight from speed or distance, 

respectively. Remember that an object thrown into the air represents two mirror-image flights, one up 

and the other down. 

4.3

Page 3 of 3 

Time from velocity 

Time from distance 

Original equation Rearranged equation to solve for time 

v = v0+ gt 

t = 

v – v0 ------------g 

y 

1 

--gt 

2 

2 

= t = 

2y 

----g 

7. At about 55 meters per second, a falling parachuter (before the parachute opens) no longer accelerates. Air 

friction opposes acceleration. Although the effect of air friction begins gradually, imagine that the parachuter 

is free falling until terminal speed (the constant falling speed) is reached. How long would that take? 

8. The climber dropped her compass at the end of her 240-meter climb. How long did it take to strike bottom? 

4.3

Name: Date: 

5.1 Ratios and Proportions 

Professional chefs use ratios and proportions daily to figure out how much of various ingredients they will need 

to make a particular dish. They may serve the same dessert one day to a wedding party with 300 guests, and 

another day to a dinner party for eight people. Ratios and proportions help them figure out the right quantities of 

ingredients to buy for each meal. In this skill sheet, you will practice converting a recipe for different group sizes. 

A recipe for Double Fudge Brownies 

Ingredients: 

3 /4 c. sugar 2 eggs 

6 tablespoons unsalted butter 1 teaspoon vanilla extract 

2 tablespoons milk 

2 cups semi-sweet chocolate chips 

3 /4 cup all-purpose flour 

1 /3 teaspoon baking soda 

1 /4 teaspoon salt 2 tablespoons confectioner’s sugar 

Makes 16 brownies. 

1. What is the ratio of milk to chocolate chips in the recipe above? 

2 

-------------------------------tablespoons 

2 cups 

2. When we know the ratios, we can make proportions by setting two ratios equal to one another. This will help 

us to find missing answers. 

Suppose Patricia needs only 8 brownies and doesn’t want any leftovers. Find out how much of each 

ingredient she needs. The original recipe will make 16 brownies. You will use the ratio of 8 / 16 = 1 / 2 to find 

the amount for each of the ingredients. Use cross-multiplication to solve the proportions. 

For flour: 

Step 1 

Step 2 

Step 3 

Step 4 

Step 5 Patricia needs 3 ----- 

8 

16 

= --------x 

3 ⁄ 4 

3 

8 × -- 

4 

= 16x 

6 = 16x 

----- 

6 

16 

= 

16x 

-------- 

16 

3 

-- 

8 

= 

x 

/ 8 cup of flour to 

make 8 brownies. 

5.1

Page 2 of 2 

1. What is the ratio of unsalted butter to eggs? 

For every __________ tablespoons of butter, you will need __________ eggs. 

2. What is the ratio of flour to baking soda? 

For every __________ cups of flour, you will need __________ teaspoon of baking soda. 

3. What is the ratio of salt to flour? 

For every __________ teaspoon(s) of salt, you will need __________ cups of flour 

4. Find the correct amount of each ingredient to make 8 brownies ( 1 / 2 of the recipe). 

Flour 

Sugar 

Butter 

Milk 

Chocolate chips 

Eggs 

Vanilla extract 

Baking soda 

Salt 

Ingredient Amount 

Confectioner’s sugar 

3 /8 cup 

5. Why are the eggs and confectioner’s sugar amounts easy to work with to make 8 brownies? 

6. Patricia has a little extra of all the ingredients. How many brownies can be made using 3 cups of chocolate 

chips? 

7. How much vanilla will she need when she makes the batch of brownies using 3 cups of chocolate chips? 

5.1

Name: Date: 

5.1 Internet Research Skills 

The Internet is a valuable tool for finding answers to your questions about the world. A search engine is like an 

on-line index to information on the World Wide Web. There are many different search engines to choose from. 

Search engines differ in how often they are updated, how many documents they contain in their index, and how 

they search for information. Your teacher may suggest several search engines for you to try. 

Search engines ask you to type a word or phrase into a box known as a field. Knowing how search engines work 

can help you pinpoint the information you need. However, if your phrase is too vague, you may end up with a lot 

of unhelpful information. 

How could you find out who was the first woman to participate in a space shuttle flight? 

First, put key phrases in quotation marks. You want to know about the “first woman” on a “space shuttle.” 

Quotation marks tell the engine to search for those words together. 

Second, if you only want websites that contain both phrases, use a + sign between them. Typing “first woman” 

+ “space shuttle” into a search engine will limit your search to websites that contain both phrases. 

If you want to broaden your search, use the word or between two terms. For example, if you type “first female” 

or “first woman” + “space shuttle” the search engine will list any website that contains either of the first two 

phrases, as long as it also contains the phrase “space shuttle.” 

You can narrow a search by using the word not. For example, if you wanted to know about marine mammals 

other than whales, you could type “marine mammals” not “whales” into the field. Please note that some search 

engines use the minus sign (-) rather than the word not. 

1. If you wanted to find out about science museums in your state that are not in your own city or town, what 

would you type into the search engine? 

2. If you wanted to find out which dog breeds are inexpensive, what would you type into the search engine? 

3. How could you research alternatives to producing electricity through the combustion of coal or natural gas? 

5.1

Page 2 of 2 

The quality of information found on the Internet varies widely. This section will give you some things 

to think about as you decide which sources to use in your research. 

1. Authority: How well does the author know the subject matter? If you search for “Newton’s laws” on the 

Internet, you may find a science report written by a fifth grade student, and a study guide written by a college 

professor. Which website is the most authoritative source? 

Museums, national libraries, government sites, and major, well-known “encyclopedia sources” are good 

places to look for authoritative information. 

2. Bias: Think about the author’s purpose. Is it to inform, or to persuade? Is it to get you to buy something? 

Comparing several authoritative sources will help you get a more complete understanding of your subject. 

3. Target audience: For whom was this website written? Avoid using sites designed for students well below 

your grade level. You need to have an understanding of your subject matter at or above your own grade 

level. Even authoritative sites for younger students (children’s encyclopedias, for example) may leave out 

details and simplify concepts in ways that would leave gaps in your understanding of your subject. 

4. Is the site up-to-date, clear, and easy to use? Try to find out when the website was created, and when it 

was last updated. If the site contains links to other sites, but those links don’t work, you may have found a 

site that is infrequently or no longer maintained. It may not contain the most current information about your 

subject. Is the site cluttered with distracting advertisements? You may wish to look elsewhere for the 

information you need. 

1. What is your favorite sport or activity? Search for information about this sport or activity. List two sites that 

are authoritative and two sites that are not authoritative. Explain your reasoning. Finally, write down the best 

site for finding out information about your favorite sport. 

2. Search for information about a physical science topic of your choice on the Internet (i.e., “simple machines,” 

“Newton’s Laws,” “Galileo”). Find one source that you would NOT consider authoritative. Write the key 

words you used in your search, the web address of the source, and a sentence explaining why this source is 

not authoritative. 

3. Find a different source that is authoritative, but intended for a much younger audience. Write the web 

address and a sentence describing who you think the intended audience is. 

4. Find three sources that you would consider to be good choices for your research here. Write two to three 

sentence description of each. Describe the author, the intended audience, the purpose of the site, and any 

special features not found in other sites. 

5.1

Name: Date: 

5.1 Preparing a Bibliography 

When you write a research paper or prepare a presentation for your class, it is important to document your 

sources. A bibliography serves two purposes. First, a bibliography gives credit to the authors who wrote the 

material you used to learn about your subject. Second, a bibliography provides your audience with sources they 

can use if they would like to learn more about your subject. 

This skill sheet provides bibliography formats and examples for various types of research materials you may use 

when preparing science papers and presentations. 

Books: 

Author last name, First name. (Year published). Title of book. Place of publication: Name of publisher. 

Vermeij, Geerat. (1997). Privileged Hands: A Scientific Life. New York: W.H. Freeman and Company. 

Newspaper and Magazine Articles: 

Author listed: 

Author last name, First name. (Date of publication). Title of Article. Title of Newspaper or Magazine, page 

# or #’s. 

Searcy, Dionne. (2006, March 20). Wireless Internet TV Is Launched in Oklahoma. The Wall Street Journal, 

p. B4. 

Brody, Jane. (2006, February/March). 10 Kids’ Nutrition Myth Busters. Nick Jr Family Magazine, pp. 72–73. 

No author listed: 

Title of article. (Date of publication). Title of Newspaper or Magazine, page # or #’s. 

Chew on this: Gum may speed recovery. (2006, March 20). St. Louis Post-Dispatch, p.H2. 

Adventures in Turning Trash into Treasure: (2006, April). Reader’s Digest, p. 24. 

5.1

Page 2 of 2 

Online Newspaper or Magazine: 


Author last name, First name. (Date of publication). Title of Article. Title of Newspaper or Magazine, 

Retrieved date, from web address. 

Dybas, Cheryl Lyn. (2006, March 20). Early Spring Disturbing Life on Northern Rivers. The Washington Post, 

Retrieved March 22, 2006, from www.washingtonpost.com. 

No author listed: 

Title of Article. (Date of publication). Title of Newspaper or Magazine. Retrieved date, from web address. 

Comet mystery turns from hot to cold. (2006, March 20). The Boston Globe, retrieved March 22, 2006, from 

Boston.com. 

Online document: 


Author last name, author first name. (Date of publication). Title of document. Retrieved date, from web 

address. 

Martinez, Carolina. (2006, March 9). NASA’s Cassini Discovers Potential Liquid Water on Enceladus. Retrieved 

March 22, 2006, from http://www.nasa.gov/mission_pages/cassini/media/cassini-20060309.html 

No Author listed: 

Organization responsible for website. (Date of publication). Title of document. Retrieved date, from web 

address. 

National Science Foundation. (2005, December 15). A fish of a different color. Retrieved March 22, 2206 from 

http://www.nsf.gov/news/news_summ.jsp?cntn_id=105661&org=NSF&from=news. 

5.1

Name: Date: 

5.1 Mass vs. Weight 

What is the difference between mass and weight? 

Weightlessness: When a diver dives off of a 10-meter diving board, she is in free-fall. If she jumped off the board 

with a scale attached to her feet, the scale would read zero even though she is under the influence of gravity. She 

is “weightless” because her feet have nothing to push against. Similarly, astronauts and everything inside a space 

shuttle seem to be weightless because they are in constant free fall. The space shuttle moves at high speed, 

therefore its constant fall toward Earth results in an orbit around the planet. 

• On Earth’s surface, the force of gravity acting on one kilogram is 2.2 pounds. So, if an object has a mass of 

2.0 kilograms, the force of gravity acting on that mass on Earth will be: 

• On the moon’s surface, the force of gravity is about 0.37 pounds per kilogram. The same object, if it were 

carried to the moon, would have a mass of 2.0 kilograms, but its weight would be just 0.74 pounds. 

1. What is the weight (in pounds) of a 7.0-kilogram bowling ball on Earth’s surface? 

2. What is the weight (in pounds) of a 7.0-kilogram bowling ball on the surface of the moon? 

3. What is the mass of a 7.0-kilogram bowling ball on the surface of the moon? 

4. Would a balance function correctly on the moon? Why or why not? 

Challenge Question 

mass weight 

• Mass is a measure of the amount of matter in an 

object. Mass is not related to gravity. 

• The mass of an object does not change when it 

is moved from one place to another. 

• Mass is commonly measured in grams or 

kilograms. 

5. Take a bathroom scale into an elevator. Step on the scale. 

• Weight is a measure of the gravitational force 

between two objects. 

• The weight of an object does change when the 

amount of gravitational force changes, as when an 

object is moved from Earth to the moon. 

• Weight is commonly measured in newtons or pounds. 

0.37 pounds 

2.0 kg × = 4.4 pounds 

kg 

0.37 pounds 

2.0 kg × = 

0.74 pounds 

kg 

a. What happens to the reading on the scale as the elevator begins to move upward? to move downward? 

b. What happens to the reading on the scale when the elevator stops moving? 

c. Why does your weight appear to change, even though you never left Earth’s gravity? 

5.1

Name: Date: 

5.1 Mass, Weight, and Gravity 

How do we define mass, weight, and gravity? 

How are mass, weight, and gravity related? 

The weight equation W = mg shows that an object’s weight (in newtons) is equal to its mass (in kilograms) 

multiplied by the strength of gravity (in newtons per kilogram) where the object is located. The weight equation 

can be rearranged to find weight, mass, or the strength of gravity if you know any two of the three. 

• Calculate the weight (in newtons) of a 5.0-kilogram backpack on Earth (g = 9.8 N/kilogram). 

Solution: 

• The same backpack weighs 8.2 newtons on Earth’s moon. What is the strength of gravity on the moon? 

Solution: 

mass weight gravity 

• Mass is a measure of the 

amount of matter in an 

object. Mass is not related 

to gravity. 

• The mass of an object does 

not change when it is 

moved from one place to 

another. 

• Mass is commonly 

measured in grams or 

kilograms. 

• Weight is a measure of the 

gravitational force between two 

objects. 

• The weight of an object does 

change when the amount of 

gravitational force changes, as 

when an object is moved from 

Earth to the moon. 

• Weight is commonly measured 

in newtons or pounds. 

5.1 

• The force that causes all masses 

to attract one another. The 

strength of the force depends on 

the size of the masses and their 

distance apart. 

Use... if you want to find... and you know... 

W = mg weight (W) mass (m) and strength of gravity (g) 

m = W/g mass (m) weight (W) and strength of gravity 

(g) 

g = W/m strength of gravity (g) weight (W) and mass (m) 

W = m( g) 

W = (5.0 kg)(9.8 N/kg) 

W = 49N 

g = W/ m 

g = 8.2 N/5.0 kg 

g = 

1.6 N/kg

Page 2 of 2 

1. A physical science textbook has a mass of 2.2 kilograms. 

a. What is its weight on Earth? 

b. What is its weight on Mars? (g = 3.7 N/kg) 

c. If the textbook weighs 19.6 newtons on Venus, what is the strength of gravity on that planet? 

2. An astronaut weighs 104 newtons on the moon, where the strength of gravity is 1.6 newtons per kilogram. 

a. What is her mass? 

b. What is her weight on Earth? 

c. What would she weigh on Mars? 

3. Of all the planets in our solar system, Jupiter has the greatest gravitational strength. 

a. If a 0.500-kilogram pair of running shoes would weigh 11.55 newtons on Jupiter, what is the strength of 

gravity there? 

b. If the same pair of shoes weighs 0.3 newtons on Pluto (a dwarf planet), what is the strength of gravity 

there? 

c. What does the pair of shoes weigh on Earth? 

4. A tractor-trailer truck carrying boxes of toy rubber ducks stops at a weigh station on the highway. The driver 

is told that the truck weighs 44,000. pounds. 

a. If there are 4.448 newtons in a pound, what is the weight of the toy-filled truck in newtons? 

b. What is the mass of the toy-filled truck? 

c. The truck drops off its load of toys, then stops at a second weigh station. Now the truck weighs 

33,000. pounds. What is its weight in newtons? 

d. Challenge! Find the total mass of the rubber duck-filled boxes that were carried by the truck. 

5.1

Name: Date: 

5.1 Gravity Problems 

In this skill sheet, you will practice using proportions as you learn more about the strength of gravity on different 

planets. 

Comparing the strength of gravity on the planets 

Table 1 lists the strength of gravity on each planet in our solar system. We can see more clearly how these values 

compare to each other using proportions. First, we assume that Earth’s gravitational strength is equal to “1.” 

Next, we set up the proportion where x equals the strength of gravity on another planet (in this case, Mercury) as 

compared to Earth. 

1 

x 

= 

Earth gravitational strength Mercury gravitational strength 

1 x 

= 

9.8 N/kg 3.7 N/kg 

(1× 3.7 N/kg) = (9.8 N/kg × x) 

3.7 N/kg 

= x 

9.8 N/kg 

0.38 = 

x 

Note that the units cancel. The result tells us that Mercury’s gravitational strength is a little more than a third of 

Earth’s. Or, we could say that Mercury’s gravitational strength is 38% as strong as Earth’s. 

Now, calculate the proportions for the remaining planets. 

Table 1: The strength of gravity on planets in our solar system 

Planet Strength of gravity 

(N/kg) 

Value compared to Earth’s 

gravitational strength 

Mercury 3.7 0.38 

Venus 8.9 

Earth 9.8 1 

Mars 3.7 

Jupiter 23.1 

Saturn 9.0 

Uranus 8.7 

Neptune 11.0 

Pluto 0.6 

5.1

Page 2 of 2 

How much does it weigh on another planet? 

Use your completed Table 1 to solve the following problems. 

Example: 

• A bowling ball weighs 15 pounds on Earth. How much would this bowling ball weigh on Mercury? 

Weight on Earth 1 

= 

Weight on Mercury 0.38 

1 15 pounds 

= 

0.38 x 

0.38× 15 pounds = x 

x = 5.7 pounds 

1. A cat weighs 8.5 pounds on Earth. How much would this cat weigh on Neptune? 

2. A baby elephant weighs 250 pounds on Earth. How much would this elephant weigh on Saturn? Give your 

answer in newtons (4.48 newtons = 1 pound). 

3. On Pluto, a baby would weigh 2.7 newtons. How much does this baby weigh on Earth? Give your answer in 

newtons and pounds. 

4. Imagine that it is possible to travel to each planet in our solar system. After a space “cruise,” a tourist returns 

to Earth. One of the ways he recorded his travels was to weigh himself on each planet he visited. Use the list 

of these weights on each planet to figure out the order of the planets he visited. On Earth he weighs 

720 newtons. List of weights: 655 N; 1,699 N; 806 N; 43 N; and 662 N. 

Challenge: Using the Universal Law of Gravitation 

Here is an example problem that is solved using 

the equation for Universal Gravitation. 

Example 

What is the force of gravity between Pluto and 

Earth? The mass of Earth is 6.0 × 10 24 kg. The 

mass of Pluto is 1.3 × 10 22 kg. The distance 

between these two planets is 5.76 × 10 12 meters. 

Force of gravity between Earth and Pluto 

Now use the equation for Universal Gravitation to solve this problem: 

6.67 10 -11 

× N-m 2 

kg 2 

⎛ ⎞ 

⎜------------------------------------------ 6.0 10 

⎟ 

⎝ ⎠ 

24 

( × kg) 

1.3 10 22 

× ( × kg) 

5.76 10 12 

( × m) 

2 

= 

----------------------------------------------------------------------------- 

Force of gravity 

52.0 10 35 

× 

33.2 10 24 

-------------------------- 1.57 10 

× 

11 = = 

× N 

5. What is the force of gravity between Jupiter and Saturn? The mass of Jupiter is 6.4 × 10 24 kg. The mass of 

Saturn is 5.7 × 10 26 kg. The distance between Jupiter and Saturn is 6.52 × 10 11 m. 

5.1

Name: Date: 

5.1 Universal Gravitation 

The law of universal gravitation allows you to calculate the gravitational force between two objects from their 

masses and the distance between them. The law includes a value called the gravitational constant, or “G.” This 

value is the same everywhere in the universe. Calculating the force between small objects like grapefruits or huge 

objects like planets, moons, and stars is possible using this law. 

What is the law of universal gravitation? 

The force between two masses m 1 and m 2 that are separated by a distance r is given by: 

So, when the masses m 1 and m 2 are given in kilograms and the distance r is given in meters, the force has the 

unit of newtons. Remember that the distance r corresponds to the distance between the center of gravity of 

the two objects. 

For example, the gravitational force between two spheres that are touching each other, each with a radius of 

0.300 meter and a mass of 1,000. kilograms, is given by: 

= 

× 1,000. kg 1,000. kg 

F 6.67 10 11 

– N-m 2 kg 2 

⁄ 

× 

( 0.300 m + 0.300 m) 

2 

---------------------------------------------------- = 0.000185 N 

Note: A small car has a mass of approximately 1,000. kilograms. Try to visualize this much mass 

compressed into a sphere with a diameter of 0.300 meters (30.0 centimeters). If two such spheres were 

touching one another, the gravitational force between them would be only 0.000185 newtons. On Earth, this 

corresponds to the weight of a mass equal to only 18.9 milligrams. The gravitational force is not very strong! 

5.1

Page 2 of 2 

Answer the following problems. Write your answers using scientific notation. 

1. Calculate the force between two objects that have masses of 70. kilograms and 2,000. kilograms. Their 

centers of gravity are separated by a distance of 1.00 meter. 

2. Calculate the force between two touching grapefruits each with a radius of 0.080 meters and a mass of 

0.45 kilograms. 

3. Calculate the force between one grapefruit as described above and Earth. Earth has a mass of 

5.9742 × 10 24 kilograms and a radius of 6.3710 × 10 6 meters. Assume the grapefruit is resting on Earth’s 

surface. 

4. A man on the moon with a mass of 90. kilograms weighs 146 newtons. The radius of the moon is 

1.74 × 106 meters. Find the mass of the moon. 

5. For m = 5.9742 × 1024 kilograms and r = 6.3710 × 106 meters, what is the value given by: G ? 

a. Write down your answer and simplify the units. 

b. What does this number remind you of? 

c. What real-life values do m and r correspond to? 

m 

r 2 

---- 

6. The distance between the centers of Earth and its moon is 3.84 × 10 8 meters. Earth’s mass is 

5.9742 × 10 24 kilograms and the mass of the moon is 7.36 × 10 22 kilograms. What is the force between Earth 

and the moon? 

7. A satellite is orbiting Earth at a distance of 35.0 kilometers. The satellite has a mass of 500. kilograms. What 

is the force between the planet and the satellite? Hint: Recall Earth’s mass and radius from earlier problems. 

8. The mass of the sun is 1.99 × 10 30 kilograms and its distance from Earth is 150. million kilometers 

(150. × 10 9 meters). What is the gravitational force between the sun and Earth? 

5.1

Name: Date: 

5.2 Friction 

Just about every move we make involves friction of some sort. This skill sheet will provide you with the 

opportunity to practice identifying the friction force(s) involved in real-world situations. 

Marco and his dad are unloading cinder blocks from the back of their pickup truck. They need to haul the blocks 

across the grass to their backyard, where they are going to make a sandbox for Marco’s younger sister. Marco 

would like to haul a bunch of blocks at once. In the garage, he finds a plastic sled and his sister’s red wagon. 

• Which type of friction would resist Marco’s motion if he pulled the blocks in the sled? 

Solution: Sliding friction. 

1. Answer these additional questions about Marco’s sandbox building project. 

a. Which type of friction would resist Marco’s motion if he pulled the blocks in the wagon? 

b. Do you think it would take more force to transport five blocks in the sled or in the wagon? Why? 

c. Would the friction force increase, decrease, or stay the same if Marco added two more blocks to the sled 

or wagon? Explain your answer. 

d. Marco tries piling twelve cinder blocks into the wagon. He pulls and pulls but the wagon doesn’t move. 

What type of force is resisting motion now? 

2. Brianna is rowing a small boat across a pond. The air is calm; there is no wind blowing. 

a. What type of friction is resisting her motion? 

b. If two friends join her in the boat, will the friction force change? Why or why not? 

3. A freight train speeds along the railroad tracks at 150 km/hr. 

a. Name two types of friction resisting this motion. 

b. If this train were replaced with a mag-lev train, which type of friction would be eliminated? 

4. Research: Some sports cars are designed with rear spoiler to make the car more stable when turning, 

accelerating, and braking. 

a. Use the Internet or your local library to find an illustration of a spoiler to share with your class. 

b. Does the spoiler increase or decrease friction between the rear tires and the road? 

c. Some small hybrid cars and sport utility vehicles also have spoilers. What is their purpose? Is it the 

same or different from the spoiler on a sports car? 

5.2

Name: Date: 

5.3 Equilibrium 

When all forces acting on a body are balanced, the forces are in equilibrium. This skill 

sheet provides free-body diagrams for you to use for practice in working with 

equilibrium. 

Remember that an unbalanced force results in acceleration. Therefore, the forces 

acting on an object that is not accelerating must be balanced. These objects may be at 

rest, or they could be moving at a constant velocity. Either way, we say that the forces 

acting on these objects are in equilibrium. 

What force is necessary in the free-body diagram at right to achieve equilibrium? 

Looking for 

The unknown force: ? N 

Given 

600 N is pressing down on the box. 

400 N is pressing up on the box. 

Relationship 

You can solve equilibrium problems using simple equations: 

600 N = 400 N + ?N 

1. Supply the missing force 

necessary to achieve 

equilibrium. 

Solution 

600 N = 400 N + ?N 

600 N – 400 N = 400 N – 400 N + ? N 

200 N = ?N 

5.3

Page 2 of 2 

2. Supply the missing forces necessary to achieve equilibrium. 

3. In the picture, a girl with a weight of 540 N is balancing on her bike in equilibrium, not moving at all. If the 

force exerted by the ground on her front wheel is 200 N, how much force is exerted by the ground on her 

back wheel? 

Challenge Question: 

4. Helium balloons stay the same size as you hold them, but swell and burst 

as they rise to high altitudes when you let them go. Draw and label force 

arrows inside and/or outside the balloons on the graphic at right to show 

why the near Earth balloon does not burst, but the high altitude balloon 

does eventually burst. Hint: What are the forces on the inside of the 

balloon? What are the forces on the outside of the balloons? 

5.3

Name: Date: 

6.1 Net Force and Newton’s First Law 

Newton’s first law tells us that when the net force is zero, objects at rest stay at rest and objects in motion keep 

moving with the same speed and direction. Changes in motion come from unbalanced forces. 

In this skill sheet, you will practice identifying balanced and unbalanced forces in everyday situations. 

• An empty shopping cart is pushed along a grocery store aisle at constant velocity. Find the cart’s weight and 

the friction force if the shopper produces a force of 40.0 newtons between the wheels and the floor, and the 

normal force on the cart is 105 newtons. 

1. Looking for: You are asked for the cart’s weight and the friction force. 

2. Given: You are given the normal force and the force produced by the shopper pushing the 

cart. 

3. Relationships: Newton’s first law states that if the shopping cart is moving at a constant velocity, the 

net force must be zero. 

4. Solution: The weight of the cart balances the normal force. Therefore, the weight of the cart is a 

downward force: -105 N. The forward force produced by the shopper balances the 

friction force, so the friction force is -40.0 N. 

1. Identify the forces on the same cart at rest. 

2. While the cart is moving along an aisle, it comes in contact with a smear of margarine that had recently been 

dropped on the floor. Suddenly the friction force is reduced from -40.0 newtons to -20.0 newtons. What is 

the net force on the cart if the “pushing force” remains at 40.0 newtons? Does the grocery cart move at 

constant velocity over the spilled margarine? 

3. Identify the normal force on the shopping cart after 75 newtons of groceries are added to the cart. 

4. The shopper pays for his groceries and pushes the shopping cart out of the store, where he encounters a ramp 

that helps him move the cart from the sidewalk down to the parking lot. What force accelerates the cart down 

the ramp? 

5. Compare the friction force on the cart when it is rolling along the blacktop parking lot to the friction force on 

the cart when it is inside the grocery store (assume the flooring is smooth vinyl tile). 

6. Why is it easy to get one empty cart moving but difficult to get a line of 20 empty carts moving? 

6.1

Name: Date: 

6.1 Isaac Newton 

6.1 

Isaac Newton is one of the most brilliant figures in scientific history. His three laws of motion are 

probably the most important natural laws in all of science. He also made vital contributions to the fields of optics, 

calculus, and astronomy. 

Plague provides opportunity for genius 

Isaac Newton was born in 

1642 in Lincolnshire, 

England. His childhood years 

were difficult. His father died 

just before he was born. When 

he was three, his mother 

remarried and left her son to 

live with his grandparents. 

Newton bitterly resented his 

stepfather throughout his life. 

An uncle helped Newton remain in school and in 

1661, he entered Trinity College at Cambridge 

University. He earned his bachelor’s degree in 1665. 

Ironically, it was the closing of the university due to 

the bubonic plague in 1665 that helped develop 

Newton’s genius. He returned to Lincolnshire and 

spent the next two years in solitary academic pursuit. 

During this period, he made significant advances in 

calculus, worked on a revolutionary theory of the 

nature of light and color, developed early versions of 

his three laws of motion, and gained new insights into 

the nature of planetary motion. 

Fear of criticism stifles scientist 

When Cambridge reopened in 1667, Newton was 

given a minor position at Trinity and began his 

academic career. His studies in optics led to his 

invention of the reflecting telescope in the early 

1670s. In 1672, his first public paper was presented, 

on the nature of light and color. 

Newton longed for public recognition of his work but 

dreaded criticism. When another bright young 

scientist, Robert Hooke, challenged some of his 

points, Newton was furious. An angry exchange of 

words left Newton reluctant to make public more of 

his work. 

Revolutionary law of universal gravitation 

In the 1680s, Newton turned his attention to forces and 

motion. He worked on applying his three laws of 

motion to orbiting bodies, projectiles, pendulums, and 

free-fall situations. This work led him to formulate his 

famous law of universal gravitation. 

According to legend, Newton thought of the idea 

while sitting in his Lincolnshire garden. He watched 

an apple fall from a tree. He wondered if the same 

force that caused the apple to fall toward the center of 

Earth (gravity) might be responsible for keeping the 

moon in orbit around Earth, and the planets in orbit 

around the sun. 

This concept was truly revolutionary. Less than 

50 years earlier, it was commonly believed that some 

sort of invisible shield held the planets in orbit. 

Important contributor in spite of conflict 

In 1687, Newton published his ideas in a famous work 

known as the Principia. He jealously guarded the 

work as entirely his. He bitterly resented the 

suggestion that he should acknowledge the exchange 

of ideas with other scientists (especially Hooke) as he 

worked on his treatise. 

Newton left Cambridge to take a government position 

in London in 1696. His years of active scientific 

research were over. However, almost three centuries 

after his death in 1727, Newton remains one of the 

most important contributors to our understanding of 

how the universe works.

Page 2 of 2 


1. Important phases of Newton’s education and scientific work occurred in isolation. Why might this have been 

helpful to him? On the other hand, why is working in isolation problematic for developing scientific ideas? 

2. Newton began his academic career in 1667. For how long was he a working scientist? Was he a very 

productive scientist? Justify your answer. 

3. Briefly state one of Newton’s three laws of motion in your own words. Give an explanation of how this law 

works. 

4. Define the law of universal gravitation in your own words. 

5. The orbit of a space shuttle is surprisingly like an apple falling from a tree to Earth. The space shuttle is 

simply moving so fast that the path of its fall is an orbit around our planet. Which of Newton’s laws helps 

explain the orbit of a space shuttle around Earth and the orbit of Earth around the sun? 

6. Research: Newton was outraged when, in 1684, German mathematician Wilhelm Leibniz published a 

calculus book. Find out why, and describe how the issue is generally resolved today. 

6.1

Name: Date: 

6.2 Newton's Second Law 

• Newton’s second law states that the acceleration of an object is directly related to the force on it, and 

inversely related to the mass of the object. You need more force to move or stop an object with a lot of mass 

(or inertia) than you need for an object with less mass. 

• The formula for the second law of motion (first row below) can be rearranged to solve for mass and force. 

What do you want to know? What do you know? The formula you will use 

acceleration (a) force (F) and mass (m) 

mass (m) acceleration (a) and force (F) 

force (F) acceleration (a) and mass (m) 

• How much force is needed to accelerate a truck with a mass of 2,000 kilograms at a rate of 3 m/s 2 ? 

• What is the mass of an object that requires 15 N to accelerate it at a rate of 1.5 m/s 2 ? 

1. What is the acceleration of a 2,000.-kilogram truck if a force of 4,200. N is used to make it start moving 

forward? 

2. What is the acceleration of a 0.30-kilogram ball that is hit with a force of 25 N? 

3. How much force is needed to accelerate a 68-kilogram skier at 1.2 m/s 2 ? 

4. What is the mass of an object that requires a force of 30 N to accelerate at 5 m/s 2 ? 

acceleration 

5. What is the force on a 1,000.-kilogram elevator that is falling freely under the acceleration of gravity only? 

mass 

F m × a 2,000 kg 3 m/s2 × 6,000 kg-m/s2 = = = = 6,000 N 

m -- 

F 15 N 

a 1.5 m/s 2 

-------------------- 

15 kg-m/s2 1.5 m/s2 = = = -------------------------- = 

10 kg 

6. What is the mass of an object that needs a force of 4,500 N to accelerate it at a rate of 5 m/s 2 ? 

7. What is the acceleration of a 6.4-kilogram bowling ball if a force of 12 N is applied to it? 

= 

= 

force 

----------mass 

---------------------------force 

acceleration 

force = acceleration × mass 

6.2

Name: Date: 

6.3 Applying Newton’s Laws of Motion 

In the second column of the table below, write each of Newton’s three laws of motion. Use your own wording. In 

the third column of the table, describe an example of each law. To find examples of Newton’s laws, think about 

all the activities you do in one day. 

Newton’s laws of 

motion 

The first law 

The second law 

The third law 

Write the law here in your own 

words 

1. When Jane drives to work, she always places her pocketbook on the passenger’s seat. By the time she gets to 

work, her pocketbook has fallen on the floor in front of the passenger seat. One day, she asks you to explain 

why this happens in terms of physical science. What do you say? 

2. You are waiting in line to use the diving board at your local pool. While watching people dive into the pool 

from the board, you realize that using a diving board to spring into the air before a dive is a good example of 

Newton’s third law of motion. Explain how a diving board illustrates Newton’s third law of motion. 

3. You know the mass of an object and the force applied to the object to make it move. Which of Newton’s laws 

of motion will help you calculate the acceleration of the object? 

4. How many newtons of force are represented by the following amount: 3 kg · m/s 2 ? 

Select the correct answer (a, b, or c) and justify your answer. 

Example of the law 

a. 6 newtons b. 3 newtons c. 1 newton 

5. Your shopping cart has a mass of 65 kilograms. In order to accelerate the shopping cart down an aisle at 

0.30 m/s 2 , what force would you need to use or apply to the cart? 

6. A small child has a wagon with a mass of 10 kilograms. The child pulls on the wagon with a force of 

2 newtons. What is the acceleration of the wagon? 

7. You dribble a basketball while walking on a basketball court. List and describe the pairs of action-reaction 

forces in this situation. 

8. Pretend that there is no friction at all between a pair of ice skates and an ice rink. If a hockey player using 

this special pair of ice skates was gliding along on the ice at a constant speed and direction, what would be 

required for him to stop? 

6.3

Name: Date: 

6.3 Momentum 

Which is more difficult to stop: A tractor-trailer truck barreling down the 

highway at 35 meters per second, or a small two-seater sports car 

traveling the same speed? 

You probably guessed that it takes more force to stop a large truck than a 

small car. In physics terms, we say that the truck has greater momentum. 

We can find momentum using this equation: 

momentum = mass of object × velocity of object 

Velocity is a term that refers to both speed and direction. For our purposes we will assume that the vehicles are 

traveling in a straight line. In that case, velocity and speed are the same. 

The equation for momentum is abbreviated like this: P = 

m × v. 

Momentum, symbolized with a P, is expressed in units of kg · m/s; m is the mass of the object, in kilograms; and 

v is the velocity of the object in m/s. 

Use your knowledge about solving equations to work out the following problems: 

1. If the truck has a mass of 4,000. kilograms, what is its momentum? Express your answer in kg · m/s. 

2. If the car has a mass of 1,000. kilograms, what is its momentum? 

3. An 8-kilogram bowling ball is rolling in a straight line toward you. If its momentum is 16 kg · m/s, how fast 

is it traveling? 

4. A beach ball is rolling in a straight line toward you at a speed of 0.5 m/s. Its momentum is 0.25 kg · m/s. 

What is the mass of the beach ball? 

5. A 4,500.-kilogram truck travels in a straight line at 10. m/s. What is its momentum? 

6. A 1,500.-kilogram car is also traveling in a straight line. Its momentum is equal to that of the truck in the 

previous question. What is the velocity of the car? 

7. Which would take more force to stop in 10. seconds: an 8.0-kilogram ball rolling in a straight line at a speed 

of 0.2 m/s or a 4.0-kilogram ball rolling along the same path at a speed of 1.0 m/s? 

8. The momentum of a car traveling in a straight line at 25 m/s is 24,500 kg·m/s. What is the car’s mass? 

9. A 0.14-kilogram baseball is thrown in a straight line at a velocity of 30. m/s. What is the momentum of the 

baseball? 

10. Another pitcher throws the same baseball in a straight line. Its momentum is 2.1 kg · m/s. What is the 

velocity of the ball? 

11. A 1-kilogram turtle crawls in a straight line at a speed of 0.01 m/s. What is the turtle’s momentum? 

6.3

Name: Date: 

6.3 Momentum Conservation 

Just as forces are equal and opposite (according to Newton’s third law), changes in momentum are also equal and 

opposite. This is because when objects exert forces on each other, their motion is affected. 

The law of momentum conservation states that if interacting objects in a system are not acted on by outside 

forces, the total amount of momentum in the system cannot change. 

The formula below can be used to find the new velocities of objects if both keep moving after the collision. 

total momentum of a system before = total momentum of a system after 

m1v1 ( initial) 

m2v + 2 (initial) 

m1v3 (final) m2v = + 4 (final) 

If two objects are initially at rest, the total momentum of the system is zero. 

For the final momentum to be zero, the objects must have equal momenta in opposite directions. 

Example 1: What is the momentum of a 0.2-kilogram steel ball that is rolling at a velocity of 3.0 m/s? 

3 m 

momentum m× v 0.2 kg × -------s 

0.6 kg m 

= = = ⋅ --s 

Example 2: You and a friend stand facing each other on ice skates. Your mass is 50. kilograms and your friend’s 

mass is 60. kilograms. As the two of you push off each other, you move with a velocity of 4.0 m/s to the right. 

What is your friend’s velocity? 

Looking for 

Solution 

Your friend’s velocity to the left. 

Given 

Your mass of 50. kg. 

Your friend’s mass of 60. kg. 

Your velocity of 4.0 m/s to the right. 

Relationship 

m1v3 = 

the momentum of a system before a collision = 0 

0 = the momentum of a system after a collision 

0 = m1v3 + m2v4 m1v3 = – ( m2v4 ) 

– ( m2v4 ) 

m1v3 = – ( m2v4 ) 

( 50. kg) 

( 4.0 m/s) 

= – 60. kg ( ) 

200 kg-m/s 

– ( 60 kg) 

-------------------------- = v4 – 3.3 m/s = v4 ( ) v 4 

Your friend’s velocity to the left is 3.3 m/s. 

6.3

Page 2 of 2 

1. If a ball is rolling at a velocity of 1.5 m/s and has a momentum of 10.0 kg·m/s, what is the mass of 

the ball? 

2. What is the velocity of an object that has a mass of 2.5 kg and a momentum of 1,000 kg · m/s? 

3. A pro golfer hits 45.0-gram golf ball, giving it a speed of 75.0 m/s. What momentum has the golfer given to 

the ball? 

4. A 400-kilogram cannon fires a 10-kilogram cannonball at 20 m/s. If the cannon is on wheels, at what 

velocity does it move backward? (This backward motion is called recoil velocity.) 

5. Eli stands on a skateboard at rest and throws a 0.5-kg rock at a velocity of 10.0 m/s. Eli moves back at 

0.05 m/s. What is the combined mass of Eli and the skateboard? 

6. As the boat in which he is riding approaches a dock at 3.0 m/s, Jasper stands up in the boat and jumps toward 

the dock. Jasper applies an average force of 800. newtons on the boat for 0.30 seconds as he jumps. 

a. How much momentum does Jasper’s 80.-kilogram body have as it lands on the dock? 

b. What is Jasper's speed on the dock? 

7. Daryl the delivery guy gets out of his pizza delivery truck but forgets to set the parking brake. The 

2,000.-kilogram truck rolls down hill reaching a speed of 30 m/s just before hitting a large oak tree. The 

vehicle stops 0.72 s after first making contact with the tree. 

a. How much momentum does the truck have just before hitting the tree? 

b. What is the average force applied by the tree? 

8. Two billion people jump up in the air at the same time with an average velocity of 7.0 m/s. If the mass of an 

average person is 60 kilograms and the mass of Earth is 5.98 × 10 24 kilograms: 

a. What is the total momentum of the two billion people? 

b. What is the effect of their action on Earth? 

9. Tammy, a lifeguard, spots a swimmer struggling in the surf and jumps from her lifeguard chair to the sand 

beach. She makes contact with the sand at a speed of 6.00 m/s, leaving an indentation in the sand 0.10 m 

deep. 

a. If Tammy's mass is 60. kilograms, what is the momentum as she first touches the sand? 

b. What is the average force applied on Tammy by the sand beach? 

10. When a gun is fired, the shooter describes the sensation of the gun kicking. Explain this in terms of 

momentum conservation. 

11. What does it mean to say that momentum is conserved? 

6.3

Name: Date: 

6.3 Collisions and Conservation of Momentum 

The law of conservation of momentum tells us that as long as colliding objects are not influenced by outside 

forces like friction, the total amount of momentum in the system before and after the collision is the same. 

We can use the law of conservation of momentum to predict how two objects will move after a collision. Use the 

problem solving steps and the examples below to help you solve collision problems. 

Problem Solving Steps 

1. Draw a diagram. 

2. Assign variables to represent the masses and velocities of the objects before and after the collision. 

3. Write an equation stating that the total momentum before the collision equals the total after. 

4. Plug in the information that you know. 

5. Solve your equation. 

A 2,000-kilogram railroad car moving at 5 m/s collides with a 

6,000-kilogram railroad car at rest. If the cars coupled together, 

what is their velocity after the inelastic collision? 

Looking for 

v 3 = the velocity of the combined 

railroad cars after an inelastic collision 

Given 

Initial speed and mass of both cars: 

m1 = 2,000 kg, v1 = 5 m/s 

m2 = 6,000 kg, v2 = 0 m/s 

Combined mass of the two cars: 

m1 + m2 = 8,000 kg 

Relationship 

m1v1 + m2v2 = (m1 + m2)v3 Solution 

( 2000 kg) 

( 5 m/s) 

+ ( 6000 kg) 

( 0 m/s) 

= ( 2000 kg + 6000 kg)v 

3 

10,000 kg-m/s = ( 8000 kg)v 

3 

10,000 kg-m/s 

---------------------------- 

8000 kg 

= v3 10 m/s = 

v 

3 

The velocity of the two combined cars after the 

collision is 10 m/s. 

6.3

Page 2 of 2 

1. What is the momentum of a 100.-kilogram fullback carrying a football on a play at a velocity of 

3.5 m/s? 

2. What is the momentum of a 75.0-kilogram defensive back chasing the fullback at a velocity of 5.00 m/s? 

3. A 2,000-kilogram railroad car moving at 5 m/s to the east collides with a 6,000-kilogram railroad car moving 

at 3 m/s to the west. If the cars couple together, what is their velocity after the collision? 

4. A 4.0-kilogram ball moving at 8.0 m/s to the right collides with a 1.0-kilogram ball at rest. After the 

collision, the 4.0-kilogram ball moves at 4.8 m/s to the right. What is the velocity of the 1-kilogram ball? 

5. A 0.0010-kg pellet is fired at a speed of 50.0m/s at a motionless 0.35-kg piece of balsa wood. When the 

pellet hits the wood, it sticks in the wood and they slide off together. With what speed do they slide? 

6. Terry, a 70.-kilogram tailback, runs through his offensive line at a speed of 7.0 m/s. Jared, a 100-kilogram 

linebacker, running in the opposite direction at 6.0 m/s, meets Jared head-on and “wraps him up.” What is 

the result of this tackle? 

7. Snowboarding cautiously down a steep slope at a speed of 7.0 m/s, Sarah, whose mass is 50. kilograms, is 

afraid she won't have enough speed to travel up a slight uphill grade ahead of her. She extends her hand as 

her friend Trevor, who has a mass of 100. kilograms, is about to pass her traveling at 16 m/s. If Trevor grabs 

her hand, calculate the speed at which the friends will be sliding. 

8. Tex, an 85.0 kilogram rodeo bull rider is thrown from the bull after a short ride. The 520. kilogram bull 

chases after Tex at 13.0 m/s. While running away at 3.00 m/s, Tex jumps onto the back of the bull to avoid 

being trampled. How fast does the bull run with Tex aboard? 

9. Identical twins Kate and Karen each have a mass of 45 kg. They are rowing their boat on a hot summer 

afternoon when they decide to go for a swim. Kate jumps off the front of the boat at a speed of 3.00 m/s. 

Karen jumps off the back at a speed of 4.00 m/s. If the 70.-kilogram rowboat is moving at 1.00 m/s when the 

girls jump, what is the speed of the rowboat after the girls jump? 

10. A 0.10-kilogram piece of modeling clay is tossed at a motionless 0.10-kilogram block of wood and sticks. 

The block slides across a frictionless table at 15 m/s. 

a. At what speed was the clay tossed? 

b. The clay is replaced with a “bouncy” ball with the same mass. It is tossed with the same speed. The 

bouncy ball rebounds from the wooden block at a speed of 10 m/s. What effect does this have on the 

wooden block? Why? 

6.3

Name: Date: 

6.3 Rate of Change of Momentum 

Momentum is given by the expression p = mv where p is the momentum of an object of mass m moving with 

velocity v. The units of momentum are kg-m/s. Change of momentum (represented Δp) over a time interval 

(represented Δt) is also called the rate of change of momentum. 

Since, momentum is p = mv, if the mass remains constant during the time Δt, then: 

Δv 

The expression, ----- , represents change in velocity over change in time, also known as acceleration. From 

Δt 

Newton’s second law, we know that acceleration equals force divided by mass (a = F/m). Rearranging the 

equation, we see that force equals mass times acceleration (F = ma). Similarly, force (F) equals change in 

momentum over change in time. 

A mass, m, moving with velocity, v, has momentum mv. If this momentum becomes zero over some change in 

time (Δt), then there is a force, F =(mv –0)/Δt. 

• mv is the initial momentum. 

• 0 is the momentum after a change in time Δt. 

Δp 

------ m 

Δt 

Δv 

= ----- 

Δt 

F ma m Δv 

= = ----- = 

Δt 

When a car accelerates or decelerates, we feel a force that pushes back during acceleration and pushes us forward 

during deceleration. When the car brakes slowly, the force is small. However, when the car brakes quickly, the 

force increases considerably. 

Example 1. An 80-kg woman is a passenger in a car going 90 km/h. The driver puts on the brakes and the car 

comes to a stop in 2 seconds. What is the average force felt by the passenger? 

First, convert the velocity to a value that is in meters per second: 90 km/h = 25 m/s. Next, use the equation that 

relates force and momentum: 

This is a large force, and for the passenger to stay in her seat, she must be strapped in with a seat belt. 

When the stopping time decreases from 2 seconds to 1 second, the force increases to 2,000 newtons. When the 

car is involved in a crash, the change in momentum happens over a much shorter period of time, thereby creating 

very large forces on the passenger. Air bags and seat belts help by slowing down the person’s momentum change, 

resulting in smaller forces and a reduced chance for injury. Let’s look at some numbers. 

Δp 

------ 

Δt 

Δp 

Force ------ m 

Δt 

Δv 

----- 

25 0 

80 kg 

Δt 

– ( ) m/s 

= = = ----------------------------- = 

1,000 N 

2 s 

6.3

Page 2 of 3 

The car travels at 90 kilometers per hour, crashes, and comes to a stop in 0.1 seconds. The air bag 

inflates and cushions the person for 1.5 seconds. Let’s calculate the force experienced by the passenger 

in an automobile without air bags and in one case with air bags. 

• Without the air bag, the momentum change happens over 0.1 seconds. This results in a force: 

The human body is not likely to survive a force as large as this. 

• With the air bag, the force created is: 

The chances for survival are much higher. 

25 m/s 

Force = 80 kg--------------- = 2,000 N 

0.1 s 

25 m/s 

Force = 80 kg--------------- = 1,333 N 

1.5 s 

Example 2. A pile is driven into the ground by hitting it repeatedly. If the pile is hit by the driver mass at a rate of 

100 kg/s and with a speed of 10 m/s, calculate the resulting average force on the pile. 

We are told that the driver mass hits the pile at a rate of 100 kg/s. What does this mean exactly? We can have a 

100-kilogram mass hitting the pile every second, or a 50-kilogram mass hitting the pile every half-second, or a 

200-kilogram mass hitting the pile every 2 seconds. You get the idea. 

The speed (v) with which the mass hits the pile is 10 m/s. The mass (m) is 100 kilograms. Time changes occur at 

1-second intervals. The force on the pile is: 

Force m Δv 

----- 100 

Δt 

kg 

----- 10 

s 

m 

--kg 

m 

= = = 1,000 ----------- = 

1,000 N 

s 

1. A 1,000-kg wrecking ball hits a wall with a speed of 2 m/s and comes to a stop in 0.01 s. Calculate the force 

experienced by the wall. 

2. A 0.15-kg soccer ball is rolling with a speed of 10 m/s and is stopped by the frictional force between it and 

the grass. If the average friction force is 0.5 N, how long would this take? 

3. Water comes out of a fire hose at a rate of 5.0 kg/s and with a speed of 50 m/s. Calculate the force on the 

hose. (This is the force that the firefighter has to provide in order to hold the hose.) 

4. Water from a fire hose is hitting a wall straight on. The water comes out with a flow rate of 25 kg/s and hits 

the wall with a speed of 30. m/s. What is the resulting force exerted on the wall by the water? 

5. The water at Niagara Falls flows at a rate of 3.0 million kg/s. The water hits the bottom of the falls at a speed 

of 25 m/s. What is the force generated by the change in momentum of the falling water? 

s 2 

6.3

Page 3 of 3 

6. A 50.-g (0.050-kg) egg that is dropped from a height of 5.0 m will hit the floor with a speed of 

about 10. m/s. The hard floor forces the egg to stop very quickly. Let’s say that it will stop in 

0.0010 second. 

a. What is the force created on the egg? 

b. The egg will break at the force you calculated for 6(a). Imagine that a 50.-kilogram person fell down on 

the egg falling under the influence of gravity. What would the force of the person on the egg be? 

c. Do you think the egg will break if the person fell on it? Why or why not? 

d. If we now drop the egg onto a pillow, it will allow the egg to stop over a much longer time compared with 

the time it takes for it to stop on the hard surface. The weight and the velocity of the egg is still the same, 

but now the time it takes for the egg to come to rest is much longer, about 0.5 second or about 500 times 

longer than the time it took to stop on the floor. What would the force on the egg be under these 

circumstances? 

e. Do you think the egg will break when it drops on the pillow? Why or why not? 

6.3

Name: Date: 

7.1 Mechanical Advantage 

Mechanical advantage (MA) is the ratio of output force to input force for a machine. 

F 

MA = 

F 

or 

MA = 

O 

i 

output force (N) 

input force (N) 

Did you notice that the force unit involved in the calculation, the newton (N) is present in both the numerator and 

the denominator of the fraction? These units cancel each other, leaving the value for mechanical advantage 

unitless. 

newtons N 

= = 1 

newtons N 

Mechanical advantage tells you how many times a machine multiplies the force put into it. Some machines 

provide us with more output force than we applied to the machine—this means MA is greater than one. Some 

machines produce an output force smaller than our effort force, and MA is less than one. We choose the type of 

machine that will give us the appropriate MA for the work that needs to be performed. 

Example 1: A force of 200 newtons is applied to a machine in order to lift a 1,000-newton load. What is the 

mechanical advantage of the machine?a 

output force (N) 1000 N 

MA = = = 5 

input force (N) 200 N 

Machines make work easier. Work is force times distance (W = F × d). The unit for work is the newton-meter. 

Using the work equation, as shown in example 2 below, can help calculate the mechanical advantage. 

Example 2: A force of 30 newtons is applied to a machine through a distance of 10 meters. The machine is 

designed to lift an object to a height of 2 meters. If the total work output for the machine is 18 newton-meters 

(N-m), what is the mechanical advantage of the machine? 

input force = 30 N output force = (work ÷ distance) = (18 N=m ÷ 2 m) = 9N 

output force (N) 9 N 

MA = = = 

0.3 

input force (N) 30 N 

7.1

Page 2 of 2 

1. A machine uses an input force of 200 newtons to produce an output force of 800 newtons. What is 

the mechanical advantage of this machine? 

2. Another machine uses an input force of 200 newtons to produce an output force of 80 newtons. What is the 

mechanical advantage of this machine? 

3. A machine is required to produce an output force of 600 newtons. If the machine has a mechanical 

advantage of 6, what input force must be applied to the machine? 

4. A machine with a mechanical advantage of 10 is used to produce an output force of 250 newtons. What input 

force is applied to this machine? 

5. A machine with a mechanical advantage of 2.5 requires an input force of 120 newtons. What output force is 

produced by this machine? 

6. An input force of 35 newtons is applied to a machine with a mechanical advantage of 0.75. What is the size 

of the load this machine could lift (how large is the output force)? 

7. A machine is designed to lift an object with a weight of 12 newtons. If the input force for the machine is set 

at 4 newtons, what is the mechanical advantage of the machine? 

8. An input force of 50. newtons is applied through a distance of 10. meters to a machine with a mechanical 

advantage of 3. If the work output for the machine is 450 newton · meters and this work is applied through a 

distance of 3 meters, what is the output force of the machine? 

9. 200. newton·meters of work is put into a machine over a distance of 20. meters. The machine does 

150. newton·meters of work as it lifts a load 10. meters high. What is the mechanical advantage of 

the machine? 

10. A machine has a mechanical advantage of 5. If 300. newtons of input force is used to produce 

3,000. newton · meters of work, 

a. What is the output force? 

b. What is the distance over which the work is applied? 

7.1

Name: Date: 

7.1 Mechanical Advantage of Simple Machines 

We use simple machines to make tasks easier. While the output work of a simple machine can never be greater 

than the input work, a simple machine can multiply input forces OR multiply input distances (but never both at 

the same time). You can use this skill sheet to practice calculating mechanical advantage (MA) for two common 

simple machines: levers and ramps. 

The general formula for the mechanical advantage (MA) of levers: 

Or you can use the ratio of the input arm length to the output arm 

length: 

Most of the time, levers are used to multiply force to lift heavy objects. 

The general formula for the mechanical advantage (MA) of ramps: 

A ramp makes it possible to move a heavy load to a new height using less 

force (but over a longer distance). 

Example 1: A construction worker uses a board and log as a lever to lift a 

heavy rock. If the input arm is 3 meters long and the output arm is 0.75 meters 

long, what is the mechanical advantage of the lever? 

3 meters 

MA = 4 

0.75 meter = 

Example 2: Sometimes levers are used to multiply distance. For a broom, your 

upper hand is the fulcrum and your lower hand provides the input force: Notice 

the input arm is shorter than the output arm. The mechanical advantage of this 

broom is: 

3 meter 

MA = = 0.25 

0.75 meter 

A mechanical advantage less than one doesn’t mean a machine isn’t useful. It just 

means that instead of multiplying force, the machine multiplies distance. A broom 

doesn’t push the dust with as much force as you use to push the broom, but a small 

movement of your arm pushes the dust a large distance. 

o 

MA lever = 

F i (input force) 

7.1 

F (output force) 

L (length of input arm) 

i 

MA lever = 

L o (length of output arm) 

ramp length 

MA ramp = 

ramp height

Page 2 of 2 

Example 3: A 500-newton cart is lifted to a height of 1 meter 

using a 10-meter long ramp. You can see that the worker only 

has to use 50 newtons of force to pull the cart. You can figure 

the mechanical advantage in either of these two ways: 

Or using the standard formula for mechanical advantage: 

Lever problems 

1. A lever used to lift a heavy box has an input arm of 4 meters and an output arm of 0.8 meters. What is the 

mechanical advantage of the lever? 

2. What is the mechanical advantage of a lever that has an input arm of 3 meters and an output arm of 2 meters? 

3. A lever with an input arm of 2 meters has a mechanical advantage of 4. What is the output arm’s length? 

4. A lever with an output arm of 0.8 meter has a mechanical advantage of 6. What is the length of the input 

arm? 

5. A rake is held so that its input arm is 0.4 meters and its output arm is 1.0 meters. What is the mechanical 

advantage of the rake? 

6. A broom with an input arm length of 0.4 meters has a mechanical advantage of 0.5. What is the length of the 

output arm? 

7. A child’s toy rake is held so that its output arm is 0.75 meters. If the mechanical advantage is 0.33, what is 

the input arm length? 

Ramp problems 

ramp length 10 meters 

MA ramp = = = 10 

ramp height 10 meter 

output force 500 newtons 

MA = = = 

10 

input force 50 newtons 

8. A 5-meter ramp lifts objects to a height of 0.75 meters. What is the mechanical advantage of the ramp? 

9. A 10-meter long ramp has a mechanical advantage of 5. What is the height of the ramp? 

10. A ramp with a mechanical advantage of 8 lifts objects to a height of 1.5 meters. How long is the ramp? 

11. A child makes a ramp to push his toy dump truck up to his sandbox. If he uses 5 newtons of force to push the 

12-newton truck up the ramp, what is the mechanical advantage of his ramp? 

12. A ramp with a mechanical advantage of 6 is used to move a 36-newton load. What input force is needed to 

push the load up the ramp? 

13. Gina wheels her wheelchair up a ramp using a force of 80 newtons. If the ramp has a mechanical advantage 

of 7, what is the output force (in newtons)? 

14. Challenge! A mover uses a ramp to pull a 1000-newton cart up to the floor of his truck (0.8 meters high). If 

it takes a force of 200 newtons to pull the cart, what is the length of the ramp? 

7.1

Name: Date: 

7.1 Work 

In science, “work” is defined with an equation. Work is the amount of force applied to an object (in the same 

direction as the motion) over a distance. By measuring how much force you have used to move something over a 

certain distance, you can calculate how much work you have accomplished. 

The formula for work is: 

A joule of work is actually a newton·meter; both units represent the same thing: work! In fact, one joule of work 

is defined as the amount of work done by pushing with a force of one newton for a distance of one meter. 

1.0 joule = 1.0 newton × 1.0 meter = 1.0 newton ⋅ meter 

• How much work is done on a 10-N block that is lifted 5 m off the ground by a pulley? 

Solution: The force applied by the pulley to lift the block is equal to the block’s weight.We can use the 

formula W = F × d to solve the problem: 

1. In your own words, define work as a scientific term. 

2. How are work, force, and distance related? 

Work (joules) = Force (newtons) × distance (meters) 

W = F × d 

Work = 10 newtons × 5 meters = 50 newton ⋅ 

meters 

3. What are two different units that represent work? 

4. For the following situations, determine whether work was done. Write “work done” or “no work done” for 

each situation. 

a. An ice skater glides for two meters across ice. 

b. The ice skater’s partner lifts her up a distance of 1 m. 

c. The ice skater’s partner carries her across the ice a distance of 3 m. 

d. After setting her down, the ice skater’s partner pulls her across the ice a distance of 10 m. 

e. After skating practice, the ice skater lifts her 20-N gym bag up 0.5 m. 

5. A woman lifts her 100-N child up one meter and carries her for a distance of 50 m to the child’s bedroom. 

How much work does the woman do? 

6. How much work does a mother do if she lifts each of her twin babies upward 1.0 m? Each baby weighs 

90. N. 

7.1

Page 2 of 2 

7. You pull your sled through the snow a distance of 500 m with a horizontal force of 200 N. How 

much work did you do? 

8. Because the snow suddenly gets too slushy, you decide to carry your 100-N sled the rest of the way 

home. How much work do you do when you pick up the sled, lifting it 0.5 m upward? How much work do 

you do to carry the sled if your house is 800 m away? 

9. An ant sits on the back of a mouse. The mouse carries the ant across the floor for a distance of 10 m. Was 

there work done by the mouse? Explain. 

10. You decide to add up all the work you did yesterday. If you accomplished 10,000 N · m of work yesterday, 

how much work did you do in units of joules? 

11. You did 150. J of work lifting a 120.-N backpack. 

a. How high did you lift the backpack? 

b. How much did the backpack weigh in pounds? (Hint: There are 4.448 N in one pound.) 

12. A crane does 62,500 J of work to lift a boulder a distance of 25.0 m. How much did the boulder weigh? 

(Hint: The weight of an object is considered to be a force in units of newtons.) 

13. A bulldozer does 30,000. J of work to push another boulder a distance of 20. m. How much force is applied 

to push the boulder? 

14. You lift a 45-N bag of mulch 1.2 m and carry it a distance of 10. m to the garden. How much work was 

done? 

15. A 450.-N gymnast jumps upward a distance of 0.50 m to reach the uneven parallel bars. How much work did 

she do before she even began her routine? 

16. It took a 500.-N ballerina a force of 250 J to lift herself upward through the air. How high did she jump? 

17. A people-moving conveyor-belt moves a 600-N person a distance of 100 m through the airport. 

a. How much work was done? 

b. The same 600-N person lifts his 100-N carry-on bag upward a distance of 1 m. They travel another 10 m 

by riding on the “people mover.” How much work was done in this situation? 

18. Which person did the most work? 

a. John walks 1,000. m to the store. He buys 4.448 N of candy and then carries it to his friend’s house 

which is 500. m away. 

b. Sally lifts her 22-N cat a distance of 0.50 m. 

c. Henry carries groceries from a car to his house. Each bag of groceries weighs 40 N. He has 10 bags. He 

lifts each bag up 1 m to carry it and then walks 10 m from his car to his house. 

7.1

Name: Date: 

7.1 Types of Levers 

A lever is a simple machine that can be used to multiply force, multiply distance, or change the direction of a 

force. All levers contain a stiff structure that rotates around a point called the fulcrum. The force applied to a 

lever is called the input force. The force applied to a load is called the output force. 

There are three types or classes of levers. The class of a lever depends on the location of the fulcrum and input 

and output forces. The picture below shows examples of the three classes of levers. Look at each lever carefully, 

noticing the location of the fulcrum, input force, and output force. 

1. In which class of lever is the output force between the fulcrum and input force? 

2. In which class of lever is the fulcrum between the input force and output force? 

3. In which class of lever is the fulcrum on one end and the output force on the other end? 

4. Do the following for each of the levers shown below and at the top of the next page: 

a. Label the fulcrum (F). 

b. Label the location of the input force (I) and output force (O). 

c. Classify the lever as first, second, or third class. 

7.1

Page 2 of 2 

The relationship between a lever’s input force and output force depends on the length of the input arm and 

output arm. The input arm is the distance between the fulcrum and input force. The output arm is the distance 

between the fulcrum and output force. 

If the input and output arms are the same length, the forces are equal. If the input arm is longer, the input force is 

less than the output force. If the input arm is shorter, the input force is greater than the output force. 

O 

1. Label the input arm (IA) and output arm (OA) on each of the levers you labeled above and on the previous 

page. 

2. In which of the levers is the input force greater than the output force? 

3. In which of the levers is the output force greater than the input force? 

4. In which of the levers are the input and output forces equal in strength? 

5. Find two other examples of levers. Draw each lever and label the fulcrum, input force, output force, input 

arm, and output arm. State whether the input or output force is stronger. 

7.1

Name: Date: 

7.1 Gear Ratios 

A gear ratio is used to figure out the number of turns each gear in 

a pair will make based on the number of teeth each gear has. 

To calculate the gear ratio for a pair of gears that are working 

together, you need to know the number of teeth on each gear. The 

formula below demonstrates how to calculate a gear ratio. 

Notice that knowing the number of teeth on each gear allows you 

to figure out how many turns each gear will take. 

Why would this be important in figuring out how to design a 

clock that has a minute and hour hand? 

A gear with 48 teeth is connected to a gear with 12 teeth. If the 48-tooth gear makes one complete turn, how 

many times will the 12-tooth gear turn? 

Turns of output gear? 48 input teeth 

= 

One turn for the input gear 12 output teeth 

48 teeth × 1 turn 

Turns of output gear? = = 

4 turns 

12 teeth 

1. A 36-tooth gear turns three times. It is connected to a 12-tooth gear. How many times does the 12-tooth gear 

turn? 

2. A 12-tooth gear is turned two times. How many times will the 24-tooth gear to which it is connected turn? 

3. A 60-tooth gear is connected to a 24-tooth gear. If the smaller gear turns ten times, how many turns does the 

larger gear make? 

4. A 60-tooth gear is connected to a 72-tooth gear. If the smaller gear turns twelve times, how many turns does 

the larger gear make? 

5. A 72-tooth gear is connected to a 12-tooth gear. If the large gear makes one complete turn, how many turns 

does the small gear make? 

7.1

Page 2 of 2 

6. Use the gear ratio formula to help you fill in the table below. 

Table 1: Using the gear ratio to calculate number of turns 

7.1 

Input Output 

Gear ratio How many turns does How many turns does 

Gear 

(# of teeth) 

Gear 

(# of teeth) 

(Input Gear: 

Output Gear) 

the output gear make 

if the input gear turns 

3 times? 

the input gear make if 

the output gear turns 

2 times? 

24 24 

36 12 

24 36 

48 36 

24 48 

7. The problems in this section involve three gears stacked on top of each other. Once you have filled in 

Table 2, answer the questions that follow. Use the gear ratio formula to help. Remember, knowing the gear 

ratios allows you to figure out the number of turns for a pair of gears. 

Table 2: Set up for three gears 

Setup Gears Number 

of teeth 

1 Top gear 12 

Middle gear 24 

Bottom gear 36 

2 Top gear 24 



3 Top gear 12 



4 Top gear 24 



Ratio 

(top gear: 

middle gear) 

Ratio 2 

(middle gear: 

bottom gear) 

Total gear ratio 

(Ratio 1 x Ratio 2) 

8. As you turn the top gear to the right, what direction does the middle gear turn? What direction will the 

bottom gear turn? 

9. How many times will you need to turn the top gear (input) in setup 1 to get the bottom gear (output) to turn once? 

10. If you turn the top gear (input) in setup 2 two times, how many times will the bottom gear (output) turn? 

11. How many times will the middle gear (output) in setup 3 turn if you turn the top gear (input) two times? 

12. How many times will you need to turn the top gear (input) in setup 4 to get the bottom gear (output) to turn 4 

times?

Name: Date: 

7.1 Levers in the Human Body 

Your skeletal and muscular systems work together to move your body parts. Some of your body parts can be 

thought of as simple machines or levers. 

There are three parts to all levers: 

• Fulcrum - the point at which the lever rotates. 

• Input force (also called the effort) - the force applied to the lever. 

• Output force (also called the load) - the force applied by the lever to move the load. 

There are three types of levers: first class, second class and third class. In a first class lever, the fulcrum is located 

between the input force and output force. In a second class lever, the output force is between the fulcrum and the 

input force. In a third class lever, the input force is between the fulcrum and the output force. An example of each 

type of lever is shown below. 

7.1

Page 2 of 2 

The three classes of levers can be found in your body. Use 

diagrams A, B, and C to answer the questions below. Also 

label the effort (input force), fulcrum and load (output force) 

on each diagram. 

LEVER A 

1. Type of Lever: __________ 

2. How is this lever used in the body? 

LEVER B 

3. Type of Lever: __________ 


LEVER C 

5. Type of Lever: __________ 


7.1

Name: Date: 

7.1 Bicycle Gear Ratios Project 

How many gears does your bicycle really have? 

Bicycle manufacturers describe any bicycle with two gears in the front and five in the back as a ten-speed. But do 

you really get ten different speeds? In this project, you will determine and record the gear ratio for each speed of 

your bicycle. You will then write up an explanation of the importance (or lack of, in some cases) of each speed. 

You will explain what the rider experiences due to the physics of the gear ratio, and in what situation the rider 

would take advantage of that particular speed. 

To complete this project, you will need: 

• Multi-speed bicycle 


• Access to a library or the Internet for research 

• Access to a computer for work with a spreadsheet (optional) 

On a multi-speed bicycle, there are two groups of gears: the front group and the rear group. You may want to 

carefully place your bicycle upside down on the floor to better work with the gears. The seat and handlebars will 

keep the bicycle balanced. 

1. Draw a schematic diagram to show how the gears are set up on your bicycle. 

2. Now, count the number of teeth on each gear in each group. Record your data in a table on paper or in a 

computer spreadsheet. Use these questions to guide you. 

a. How many gears are in the front group? 

b. How many teeth on each gear in the front group? 

c. How many gears are in the rear group? 

d. How many teeth on each gear in the rear group? 

7.1

Page 2 of 2 

3. Now, calculate the gear ratio for each front/rear combination of gears. 

Use the formula: front gear ÷ rear gear. 

Organize the results of your calculations into a new table either on paper or in a computer 

spreadsheet. 

How many different gear ratios do you actually have? 

4. Use your library or the Internet to research the development of the multi-speed bicycle. Take careful notes 

while you do your research as you will use the information you find to write a report (see step 7). In your 

research, find the answers to the following questions. 

a. In what circumstances would a low gear ratio be helpful? Why? 

b. In what circumstances would a high gear ratio be helpful? Why? 

5. Write up your findings and results according to the guidelines below. 

Your final project should include: 

• A brief (one page) report that discusses the evolution of the bicycle. What was the first bicycle like? How 

did we end up with the modern bicycle? Why was the multi-speed bicycle an important invention? 

• A schematic diagram of your bicycle’s gears. Include labels. 

• An organized, professional data table showing the gear ratios of your bicycle. 

• A summary report (one page) in which you interpret your findings and explain the trade-off between force 

and distance when pedaling a bicycle in each of the different speeds. Include answers to questions 4(a) and 

4(b). In your research, you should make a surprising discovery about the speeds—what is it? 

• Reflection: Finish the report with one or two paragraphs that express your reflections on this project. 

7.1

Name: Date: 

7.2 Potential and Kinetic Energy 

This skill sheet reviews various forms of energy and introduces formulas for two kinds of mechanical energy— 

potential and kinetic. You will learn how to calculate the amount of kinetic or potential energy for an object. 

Forms of energy 

Forms of energy include radiant energy from the sun, chemical energy from the food you eat, and electrical 

energy from the outlets in your home. Mechanical energy refers to the energy an object has because of its motion. 

All these forms of energy may be used or stored. Energy that is stored is called potential energy. Energy that is 

being used for motion is called kinetic energy. All types of energy are measured in joules or newton-meters. 

Potential energy 

The word potential means that something is capable of becoming active. Potential energy sometimes is referred 

to as stored energy. This type of energy often comes from the position of an object relative to Earth. A diver on 

the high diving board has more energy than someone who dives into the pool from the low dive. 

The formula to calculate the potential energy of an object is the mass of the object times the acceleration due to 

gravity (9.8 m/s 2 ) times the height of the object. 

Did you notice that the mass of the object in kilograms times the acceleration of gravity (g) is the same as the 

weight of the object in newtons? Therefore you can think of an object’s potential energy as equal to the object’s 

weight multiplied by its height. 

So... 

Kinetic energy 

1 N = 1 kg i 

2 

m 

2 

s = 

1 joule= 1 kg i 1 N i m 

Kinetic energy is the energy of motion. Kinetic energy depends on the mass of the object as well as the speed of 

that object. Just think of a large object moving at a very high speed. You would say that the object has a lot of 

energy. Since the object is moving, it has kinetic energy. The formula for kinetic energy is: 

m 

2 

s 

Ep= mgh 

9.8 m 

mass of the object (kilograms) × = weight of the object (newtons) 

2 

s 

E p = weight of object × height of object 

1 

Ek= mv 

2 

2 

7.2

Page 2 of 2 

To do this calculation, square the velocity value. Next, multiply by the mass, and then divide by 2. 

How are these mechanical energy formulas used in everyday situations? Take a look at two example problems. 

• A 50 kg boy and his 100 kg father went jogging. Both ran at a rate of 5 m/s. Who had more kinetic energy? 

Show your work and explain. 

Solution: Although the boy and his father were running at the same speed, the father has more kinetic 

energy because he has more mass. 

The kinetic energy of the boy: 

The kinetic energy of the father: 

2 2 

1 ⎛5 m⎞ 

m 

(50 kg) ⎜ ⎟ = 625 kg i = 625 joules 

2 

2 ⎝ s ⎠ 

s 

2 2 

1 ⎛5 m⎞ 

m 

(100 kg) ⎜ ⎟ = 1,250 kg i = 1,250 joules 

2 

2 ⎝ s ⎠ 

s 

• What is the potential energy of a 10 N book that is placed on a shelf that is 2.5 m high? 

Solution: The book’s weight (10 N) is equal to its mass times the acceleration of gravity. Therefore, you can 

easily use this value in the potential energy formula: 

potential energy = mgh = (10 N)(2.5 m) = 25 N i 

m = 25 joules 

Now it is your turn to try calculating potential and kinetic energy. Don’t forget to keep track of the units! 

1. Determine the amount of potential energy of a 5.0-N book that is moved to three different shelves on a 

bookcase. The height of each shelf is 1.0 m, 1.5 m, and 2.0 m. 

2. You are on in-line skates at the top of a small hill. Your potential energy is equal to 1,000. J. The last time 

you checked, your mass was 60.0 kg. 

a. What is your weight in newtons? 

b. What is the height of the hill? 

c. If you start rolling down this hill, your potential energy will be converted to kinetic energy. At the bottom 

of the hill, your kinetic energy will be equal to your potential energy at the top. Calculate your speed at 

the bottom of the hill. 

3. A 1.0-kg ball is thrown into the air with an initial velocity of 30. m/s. 

a. How much kinetic energy does the ball have? 

b. How much potential energy does the ball have when it reaches the top of its ascent? 

c. How high into the air did the ball travel? 

4. What is the kinetic energy of a 2,000.-kg boat moving at 5.0 m/s? 

5. What is the velocity of an 500-kg elevator that has 4000 J of energy? 

6. What is the mass of an object traveling at 30. m/s if it has 33,750 J of energy? 

7.2

Name: Date: 

7.2 Identifying Energy Transformations 

Systems change when energy flows and changes from one part of a system to another. Parts of a system may 

speed up or slow down, get warmer or colder, or change in other measurable ways. Each change transfers energy 

or transforms energy from one form to another. In this skill sheet, you will practice identifying energy 

transformations in various systems. 

• At 5:30 a.m., Miranda’s electric alarm clock starts beeping (1). It’s still dark outside so she switches on the 

light (2). She stumbles sleepily down the hall to the kitchen (3), where she lights a gas burner on the stove 

(4) to warm some oatmeal for breakfast. 

Miranda has been awake for less than ten minutes, and she’s already participated in at least four energy 

transformations. Describe an energy transformation that took place in each of the numbered events above. 

Solution: 

1. Electrical energy to sound energy; 2. Electrical energy to radiant energy (light and heat); 3. Chemical 

energy from food to kinetic energy; 4. Chemical energy from natural gas to radiant energy (heat and light). 

1. There is a spring attached to the screen door on Elijah’s front porch. Elijah opens the door, stretching the 

spring (1). After walking through the doorway (2), Elijah lets go of the door, and the spring contracts, 

pulling the door shut (3). Describe an energy transformation that took place in each of the numbered events 

above. 

2. Name two energy transformations that occur as Gabriella heats a bowl of soup in the microwave. 

3. Dmitri uses a hand-operated air pump to inflate a small swimming pool for his younger siblings. Name two 

energy transformations that occurred. 

4. Simon puts new batteries in his radio-controlled car and its controller. He activates the controller, which 

sends a radio signal to the car. The car moves forward. Name at least three energy transformations that 

occurred. 

5. Name two energy transformations that occur as Adeline pedals her bicycle up a steep hill and then coasts 

down the other side. 

7.2

Name: Date: 

7.2 Energy Transformations—Extra Practice 

You have learned that the amount of energy in the universe is constant and that in any situation requiring energy, 

all of it must be accounted for. This is the basis for the law of conservation of energy. In this skill sheet you will 

analyze different scenarios in terms of what happens to energy. Based on your experience with the CPO energy 

car, you already know that potential energy can be changed into kinetic energy and vice versa. 

As you study the scenarios below, specify whether kinetic energy is being changed to potential energy, potential 

is being converted to kinetic, or neither. Explain your answers. 

For each scenario, see if you can also answer the following questions: Are other energy transformations 

occurring? In each scenario, where did all the energy go? 

• A roller coaster car travels from point A to point B. 

Solution: 

First, potential energy is changed into kinetic energy 

when the roller coaster car rolls down to the bottom of 

the first hill. But when the car goes up the second hill to 

point B, kinetic energy is changed to potential energy. 

Some energy is lost to friction. That is why point B is a little lower than point A. 

1. A bungee cord begins to exert an upward force on a falling 

bungee jumper. 

2. A football is spiraling downward toward a football player. 

3. A solar cell is charging a battery. 

7.2

Page 2 of 2 

Energy Scenarios 

7.2 

Read each scenario below. Then complete the following for each scenario: 

• Identify which of the following forms of energy are involved in the scenario: 

mechanical, radiant, electrical, chemical, and nuclear. 

• Make an energy flow chart that shows how the energy changes from one form to another, in the correct order. 

Use a separate paper and colored markers to make your flow charts more interesting. 

• In Western states, many homes generate electricity from 

windmills. In a particular home, a young boy is using the 

electricity to run a toy electric train. 

Solution: 

Mechanical energy of the windmill is changed to electrical energy which is changed to the mechanical 

energy of the toy train. 

1. A camper is using a wood fire to heat up a pot of water for 

tea. The pot has a whistle that lets the camper know when the 

water boils. 

2. The state of Illinois generates some of its electricity from 

nuclear power. A young woman in Chicago is watching a 

broadcast of a sports game on television. 

3. A bicyclist is riding at night. He switches on his bike’s 

generator so that his headlight comes on. The harder he 

pedals, the brighter his headlight glows.

Name: Date: 

7.2 Conservation of Energy 

The law of conservation of energy tells us that energy can never be created or destroyed—it is just transformed 

from one form to another. The total energy after a transformation (from potential to kinetic energy, for example) 

is equal to the total energy before the transformation. We can use this law to solve real-world problems, as shown 

in the example below. 

• A 0.50-kilogram ball is tossed upward with a kinetic energy of 100. joules. How high does the ball travel? 

1. Looking for: The maximum height of the ball. 

2. Given: The mass of the ball, 0.50 kg, and the kinetic energy at the start: 100. joules 

3. Relationships: E K = 1 / 2mv 2 ; E p = mgh 

4. Solution: The potential energy at the top of the ball’s flight is equal to its kinetic energy at the 

start. Therefore, E p = mgh = 100. joules. 

Substitute into the equation m = 0.50 kg and g = 9.8 m/s 2 . 

100. = mgh = (0.50)(9.8)h = 4.9h 

Solve for h. 

100. = 4.9h; 100.÷ 4.9 = h 

h = 20. m 

1. A 3.0-kilogram toy dump truck moving with a speed of 2.0 m/s starts up a ramp. How high does the truck 

roll before it stops? 

2. A 2.0-kilogram ball rolling along a flat surface starts up a hill. If the ball reaches a height of 0.63 meters, 

what was its initial speed? 

3. A 500.-kilogram roller coaster starts from rest at the top of an 80.0-meter hill. What is its speed at the bottom 

of this hill? 

4. Find the potential energy of this roller coaster when it is halfway down the hill. 

5. A 2.0-kilogram ball is tossed straight up with a kinetic energy of 196 joules. How high does it go? 

6. A 50.-kilogram rock rolls off the edge of a cliff. If it is traveling at a speed of 24.2 m/s when it hits the 

ground, what is the height of the cliff? 

7. Challenge! Make up your own energy conservation problem. Write the problem and the answer on separate 

index cards. Exchange problem cards with a partner. Solve the problems and then check each other’s work 

using the answer cards. If your answers don’t agree, work together to find the source of error. 

7.2

Name: Date: 

7.2 James Prescott Joule 

7.2 

James Joule was known for the accuracy and precision of his work in a time when exactness of 

measurements was not held in high regard. He demonstrated that heat is a form of energy. He studied the 

nature of heat and the relationship of heat to mechanical work. Joule has also been credited with finding the 

relationship between the flow of electricity through a resistance, such as a wire, and the heat given off from it. 

This is now known as Joule’s Law. He is remembered for his work that led to the First Law of Thermodynamics 

(Law of Conservation of Energy). 

The young student 

James Joule was born near Manchester, England on 

December 24, 1818. His father was a wealthy brewery 

owner. James injured his spine when he was young 

and as a result he spent a great deal of time indoors, 

reading and studying. When he became interested in 

science, his father built him a lab in the basement. 

When James was fifteen years old, his father hired 

John Dalton, a leading scientist at the time, to tutor 

James and his brother, Benjamin. Dalton believed that 

a scientist needed a strong math background. He spent 

four years teaching the boys Euclidian mathematics. 

He also taught them the importance of taking exact 

measurements, a skill that strongly influenced James 

in his scientific endeavors. 

Brewer first, scientist second 

After their father became ill, James and Benjamin ran 

the family brewery. James loved the brewery, but he 

also loved science. He continued to perform 

experiments as a serious hobby. In his lab, he tried to 

make a better electric motor using electromagnets. 

James wanted to replace the old steam engines in the 

brewery with these new motors. 

Though he learned a lot about magnets, heat, motion, 

and work, he was not able to change the steam engines 

in the brewery. The cost of the zinc needed to make 

the batteries for the electric motors was much too 

high. Steam engines fired by coal were more cost 

efficient. 

The young scientist 

In 1840, when he was only twenty-two years old, 

Joule wrote what would later be known as Joule’s 

Law. This law explained that electricity produces heat 

when it travels through a wire due to the resistance of 

the wire. Joule’s Law is still used today to calculate 

the amount of heat produced from electricity. 

By 1841, Joule focused 

most of his attention on the 

concept of heat. He 

disagreed with most of his 

peers who believed that 

heat was a fluid called 

caloric. Joule argued that 

heat was a state of vibration 

caused by the collision of 

molecules. He showed that 

no matter what kind of 

mechanical work was done, 

a given amount of mechanical work always produced 

the same amount of heat. Thus, he concluded, heat 

was a form of energy. He established this kinetic 

theory nearly 100 years before others truly accepted 

that molecules and atoms existed. 

On his honeymoon 

In 1847, Joule married Amelia Grimes, and the couple 

spent their honeymoon in the Alps. Joule had always 

been fascinated by waterfalls. He had observed that 

water was warmer at the bottom of a waterfall than at 

the top. He believed that the energy of the falling 

water was transformed into heat energy. While he and 

his new bride were in the Alps, he tried to prove his 

theory. His experiment failed because there was too 

much spray from the waterfall, and the water did not 

fall the correct distance for his calculations to work. 

From 1847–1854, Joule worked with a scientist named 

William Thomson. Together they studied 

thermodynamics and the expansion of gases. They 

learned how gases react under different conditions. 

Their law, named the Joule-Thomson effect, explains 

that compressed gases cool when they are allowed to 

expand under the right conditions. Their work later led 

to the invention of refrigeration. 

James Joule died on October 11, 1889. The international 

unit of energy is called the Joule in his honor.

Page 2 of 2 


1. Why do you think that Joule’s father built him a science lab when he was young? 

2. What evidence is there that Joule had an exceptional education? 

3. Why was Joule so interested in electromagnets? 

4. Why would you consider Joule’s early experiments with electric motors important even though he did not 

achieve his goal? 

5. Explain Joule’s Law in your own words. 

6. Describe something Joule believed that contradicted the beliefs of his peers. 

7. Describe the experiment that Joule tried to conduct on his honeymoon. 

8. Name one thing that we use today that was invented as a result of his research. 

9. What unit of measurement is named after him? 

10. Research: Find out more information about one of Joule’s more well-known experiments, and share your 

findings with the class. Try to find a picture of some of the apparatus that he used in his experiments. 

Suggested topics: galvanometer, heat energy, kinetic energy, mechanical work, conservation of energy, 

Kelvin scale of temperature, thermodynamics, Joule-Thomson Effect, electric welding, electromagnets, 

resistance in wires. 

7.2

Name: Date: 

7.3 Efficiency 

In a perfect machine, the work input would equal the work output. However, there aren’t any perfect machines in 

our everyday world. Bicycles, washing machines, and even pencil sharpeners lose some input work to friction. 

Efficiency is the ratio of work output to work input. It is expressed as a percent. A perfect machine would have an 

efficiency of 100 percent. 

An engineer designs a new can opener. For every twenty joules of work input, the can opener produces ten joules 

of work output. The engineer tries different designs and finds that her improved version produces thirteen joules 

of work output for the same amount of work input. How much more efficient is the new version? 

Efficiency of the first design Efficiency of the second design 

work output 

Efficiency = 

work input 

10 joules 

= 

20 joules 

= 50% 

The second design is 15% more efficient than the first. 

work output 

Efficiency = 

work input 

13 joules 

= 

20 joules 

= 65% 

1. A cell phone charger uses 4.83 joules per second when plugged into an outlet, but only 1.31 joules per 

second actually goes into the cell phone battery. The remaining joules are lost as heat. That’s why the battery 

feels warm after it has been charging for a while. How efficient is the charger? 

2. A professional cyclist rides a bicycle that is 92 percent efficient. For every 100 joules of energy he exerts as 

input work on the pedals, how many joules of output work are used to move the bicycle? 

3. An automobile engine is 15 percent efficient. How many joules of input work are required to produce 

15,000 joules of output work to move the car? 

4. It takes 56.5 kilojoules of energy to raise the temperature of 150 milliliters of water from 5 °C to 95 °C. If 

you use an electric water heater that is 60% efficient, how many kilojoules of electrical energy will the 

heater actually use by the time the water reaches its final temperature? 

5. A power station burns 75 kilograms of coal per second. Each kg of coal contains 27 million joules of energy. 

a. What is the total power of this power station in watts? (watts = joules/second) 

b. The power station’s output is 800 million watts. How efficient is this power station? 

6. A machine requires 2,000 joules to raise a 20. kilogram block a distance of 6.0 meters. How efficient is the 

machine? (Hint: Work done against gravity = mass × acceleration due to gravity × height.) 

7.3

Name: Date: 

7.3 Power 

In science, work is defined as the force needed to move an object a certain distance. The amount of work done 

per unit of time is called power. 

Suppose you and a friend are helping a neighbor to reshingle the roof of his home. You each carry 10 bundles of 

shingles weighing 300 newtons apiece up to the roof which is 7 meters from the ground. You are able to carry the 

shingles to the roof in 10 minutes, but your friend needs 20 minutes. 

Both of you did the same amount of work (force × distance) but you did the work in a shorter time. 

However, you had more power than your friend. 

Let’s do the math to see how this is possible. 

Step one: Convert minutes to seconds. 

Step two: Find power. 

W = F× d 

W = 10 bundles of shingles (300 N/bundle) × 7 m = 21,000 joules 

Work (joules) 

Power (watts) = Time (seconds) 

60 seconds 

10 minutes × = 600 seconds (You) 

minute 

60 seconds 

20 minutes × = 1,200 seconds (Friend) 

minute 

21,000 joules 

= 35 watts (You) 

600 seconds 

21,000 joules 

= 

17.5 watts (Friend) 

1,200 seconds 

As you can see, more power is produced when the same amount of work is done in a shorter time period. You 

have probably heard the word watt used to describe a light bulb. Is it now clear to you why a 100-watt bulb is 

more powerful than a 40-watt bulb? 

7.3

Page 2 of 2 

1. A motor does 5,000. joules of work in 20. seconds. What is the power of the motor? 

2. A machine does 1,500 joules of work in 30. seconds. What is the power of this machine? 

3. A hair dryer uses 72,000 joules of energy in 60. seconds. What is the power of this hair dryer? 

4. A toaster oven uses 67,500 joules of energy in 45 seconds to toast a piece of bread. What is the power of the 

oven? 

5. A horse moves a sleigh 1.00 kilometer by applying a horizontal 2,000.-newton force on its harness for 

45.0 minutes. What is the power of the horse? (Hint: Convert time to seconds.) 

6. A wagon is pulled at a speed of 0.40 m/s by a horse exerting an 1,800-newton horizontal force. What is the 

power of this horse? 

7. Suppose a force of 100. newtons is used to push an object a distance of 5.0 meters in 15 seconds. Find the 

work done and the power for this situation. 

8. Emily’s vacuum cleaner has a power rating of 200. watts. If the vacuum cleaner does 360,000 joules of 

work, how long did Emily spend vacuuming? 

9. Nicholas spends 20.0 minutes ironing shirts with his 1,800-watt iron. How many joules of energy were used 

by the iron? (Hint: convert time to seconds). 

10. It take a clothes dryer 45 minutes to dry a load of towels. If the dryer uses 6,750,000 joules of energy to dry 

the towels, what is the power rating of the machine? 

11. A 1000-watt microwave oven takes 90 seconds to heat a bowl of soup. How many joules of energy does it 

use? 

12. A force of 100. newtons is used to move an object a distance of 15 meters with a power of 25 watts. Find the 

work done and the time it takes to do the work. 

13. If a small machine does 2,500 joules of work on an object to move it a distance of 100. meters in 

10. seconds, what is the force needed to do the work? What is the power of the machine doing the work? 

14. A machine uses a force of 200 newtons to do 20,000 joules of work in 20 seconds. Find the distance the 

object moved and the power of the machine. (Hint: A joule is the same as a Newton-meter.) 

15. A machine that uses 200. watts of power moves an object a distance of 15 meters in 25 seconds. Find the 

force needed and the work done by this machine. 

7.3

Name: Date: 

7.3 Power in Flowing Energy 

Power is the rate of doing work. You do work if you lift a heavy box up a flight of stairs. You do the same 

amount of work whether you lift the box slowly or quickly. But your power is greater if you do the work in a 

shorter amount of time. 

Power can also be used to describe the rate at which energy is converted from one form into another. A light bulb 

converts electrical energy into heat (thermal energy) and light (radiant energy). The power of a light bulb is the 

rate at which the electrical energy is converted into these other forms. 

To calculate the power of a person, machine, or other device, you must know the work done or energy converted 

and the time. Work can be calculated using the following formula: 

Both work and energy are measured in joules. A joule is actually another name for a newton·meter. If you push 

an object along the floor with a force of 1 newton for a distance of 1 meter, you have done 1 joule of work. A 

motor could be used to do this same task by converting 1 joule of electrical energy into mechanical energy. 

Power is calculated by dividing the work or energy by the time. Power is measured in watts. One watt is equal to 

one joule of work or energy per second. In one second, a 60-watt light bulb converts 60 joules of electrical energy 

into heat and light. Power can also be measured in horsepower. One horsepower is equal to 746 watts. 

A cat who cat weighs 40 newtons climbs 15 meters up a tree in 10 seconds. Calculate the work done by the cat 

and the cat’s power. 

Looking for 

Solution 

The work and power of the cat. 

Given 

The force is 40 N. 

The distance is 15 m. 

The time is 10 s. 

Relationships 

Work = Force × distance 

Power = Work/time 

Work (joules) = Force (newtons) × distance (meters) 

W = F× d 

Work or Energy (joules) 

Power (watts) = 

Time (s) 

P = W / t 

Work = 40 N × 15 m = 600 J 

600 J 

Power = 60 W 

10 s = 

The work done by the cat is 600 joules. 

The power of the cat is 60 watts. 

In units of horsepower, the cat’s power is 

(60 watts)(1 hp / 746 watts) = 0.12 horsepower. 

7.3

Page 2 of 2 

1. Complete the table below: 

Force (N) Distance (m) Time (sec) Work (J) Power (W) 

100 2 5 

100 2 10 

100 4 10 

100 25 500 

20 20 1000 

30 10 60 

9 20 60 

3 75 5 

2. Oliver weighs 600. newtons. He climbs a flight of stairs that is 3.0 meters tall in 4.0 seconds. 

a. How much work did he do? 

b. What was Oliver’s power in watts? 

3. An elevator weighing 6,000. newtons moves up a distance of 10.0 meters in 30.0 seconds. 

a. How much work did the elevator’s motor do? 

b. What was the power of the elevator’s motor in watt and in horsepower? 

4. After a large snowstorm, you shovel 2,500. kilograms of snow off of your sidewalk in half an hour. You lift 

the shovel to an average height of 1.5 meters while you are piling the snow in your yard. 

a. How much work did you do? Hint: The force is the weight of the snow. 

b. What was your power in watts? Hint: You must always convert time to seconds when calculating power. 

5. A television converts 12,000 joules of electrical energy into light and sound every minute. What is the power 

of the television? 

6. The power of a typical adult’s body over the course of a day is 100. watts. This means that 100. joules of 

energy from food are needed each second. 

a. An average apple contains 500,000 joules of energy. For how many seconds would an apple power a 

person? 

b. How many joules are needed each day? 

c. How many apples would a person need to eat to get enough energy for one day? 

7. A mass of 1,000. kilograms of water drops 10.0 meters down a waterfall every second. 

a. How much potential energy is converted into kinetic energy every second? 

b. What is the power of the waterfall in watts and in horsepower 

8. An alkaline AA battery stores approximately 12,000 joules of energy. A small flashlight uses two AA 

batteries and will produce light for 2.0 hours. What is the power of the flashlight bulb? Assume all of the 

energy in the batteries is used. 

7.3

Name: Date: 

7.3 Efficiency and Energy 

Efficiency describes how well energy is converted from one form into another. A process is 100% efficient if no 

energy is “lost” due to friction, to create sound, or for other reasons. In reality, no process is 100% efficient. 

Efficiency is calculated by dividing the output energy by the input energy. If 

you multiply the result by 100, you will get efficiency as a percentage. For 

example, if the answer you get is 0.50, you can multiply by 100 and write 

your answer as 50%. 

You drop a 2-kilogram box from a height of 3 meters. Its speed is 7 m/s when it hits the ground. How efficiently 

did the potential energy turn into kinetic energy? 

Looking for 

You are asked to find the efficiency. 

Given 

The mass is 2 kilograms, the height is 3 meters, 

and the landing speed is 7 m/s. 

Relationships 

Kinetic energy = 1/2mv 2 

Potential energy = mgh 

Efficiency = (output energy)/(input energy) 

Solution 

The input energy is the potential energy, and the 

output energy is the kinetic energy. 

The efficiency is 0.83 or 83% (0.83 × 100). 

1. Engineers who design battery-operated devices such as cell phones and MP3 players try to make them as 

efficient as possible. An engineer tests a cell phone and finds that the batteries supply 10,000 J of energy to 

make 5500 J of output energy in the form of sound and light for the screen. How efficient is the phone? 

2. What’s the efficiency of a car that uses 400,000 J of energy from gasoline to make 48,000 J of kinetic 

energy? 

3. A 1000.-kilogram roller coaster goes down a hill that is 90. meters tall. Its speed at the bottom is 40. m/s. 

a. What is the efficiency of the roller coaster? Assume it starts from rest at the top of the hill. 

b. What do you think happens to the “lost” energy? 

c. Use the concepts of energy and efficiency to explain why the first hill on a roller coaster is the tallest. 

4. You see an advertisement for a new free fall ride at an amusement park. The ad says the ride is 50. meters tall 

and reaches a speed of 28 m/s at the bottom. How efficient is the ride? Hint: You can use any mass you wish 

because it cancels out. 

5. Imagine that you are working as a roller coaster designer. You want to build a record-breaking coaster that 

goes 70.0 m/s at the bottom of the first hill. You estimate that the efficiency of the tracks and cars you are 

using is 90.0%. How high must the first hill be? 

E 

E 

P 

K 

= = 

= = 

7.3 

Output energy (J) 

Efficiency = Input energy (J) 

2 

(2 kg)(9.8 m/s )(3 m) 58.8 J 

2 

(1/ 2)(2 kg)(7 m/s) 49 J 

Efficiency = (49 J)/(58.8 J) = 

0.83 or 83%

Name: Date: 

8.2 Measuring Temperature 

How do you find the temperature of a substance? 

There are many different kinds of thermometers 

used to measure temperature. Can you think of 

some you find at home? In your classroom you 

will use a glass immersion thermometer to find 

the temperature of a liquid. The thermometer 

contains alcohol with a red dye in it so you can 

see the alcohol level inside the thermometer. 

The alcohol level changes depending on the 

surrounding temperature. You will practice 

reading the scale on the thermometer and 

report your readings in degrees Celsius. 

Safety: Glass thermometers are breakable. Handle them carefully. Overheating the thermometer can cause the 

alcohol to separate and give incorrect readings. Glass thermometers should be stored horizontally or vertically 

(never upside down) to prevent alcohol from separating. 

Reading the temperature scale correctly 

Look at the picture at right. See the close-up of the line inside the thermometer on the 

scale. The tens scale numbers are given. The ones scale appears as lines. Each small line 

equals 1 degree Celsius. Practice reading the scale from the bottom to the top. One small 

line above 20 °C is read as 21 °C. When the level of the alcohol is between two small 

lines on the scale, report the number to the nearest 0.5 °C. 


a. What number does the large line between 20 °C and 10 °C equal? Figure out by 

counting the number of small lines between 20 °C and 10 °C. 

b. Give the temperature of the thermometer in the picture above. 

Materials 

• Alcohol immersion thermometer 

• Beakers 

• Water at different temperatures 

• Ice 

c. Practice rounding the following temperature values to the nearest 0.5 °C: 

23.1 °C, 29.8 °C, 30.0 °C, 31.6 °C, 31.4 °C. 

d. Water at 0 °C and 100 °C has different properties. Describe what water looks 

like at these temperatures. 

e. What will happen to the level of the alcohol if you hold the thermometer by the 

bulb?

Page 2 of 2 

Reading the temperature of water in a beaker 

An immersion thermometer must be placed in liquid up to the solid line on the thermometer (at least 2 

and one half inches of liquid). Wait about 3 minutes for the temperature of the thermometer to equal the 

temperature of the liquid. Record the temperature to the nearest 0.5 °C when the level stops moving. 

1. Place the thermometer in the beaker. Check to make sure that the water level is above the solid line on the 

thermometer. 

2. Wait until the alcohol level stops moving (about three minutes). Record the temperature to the nearest 

0.5 °C. 

Reading the temperature of warm water in a beaker 

A warm liquid will cool to room temperature. For a warm liquid, record the warmest temperature you observe 

before the temperature begins to decrease. 

1. Repeat the procedure above with a beaker of warm (not boiling) water. 

2. Take temperature readings every 30 seconds. Record the warmest temperature you observe. 

Reading the temperature of ice water in a beaker 

When a large amount of ice is added to water, the temperature of the water will drop 

until the ice and water are the same temperature. After the ice has melted, the cold 

water will warm to room temperature. 

1. Repeat the procedure above with a beaker of ice and water. 

2. Take temperature readings every 30 seconds. Record the coldest temperature 

you observe.

Name: Date: 

8.2 Temperature Scales 

The Fahrenheit and Celsius temperature scales are commonly used scales for reporting temperature values. 

Scientists use the Celsius scale almost exclusively, as do many countries of the world. The United States relies on 

the Fahrenheit scale for reporting temperature information. You can convert information reported in degrees 

Celsius to degrees Fahrenheit or vice versa using conversion formulas. 

Fahrenheit (°F) to Celsius (°C) conversion formula: 

Celsius (°C) to Fahrenheit (°F) conversion formula: 

• What is the Celsius value for 65° Fahrenheit? 

Solution: 

• 200 °C is the same temperature as what value on the Fahrenheit scale? 

Solution: 

o 

⎛5⎞ C = ⎜ ⎟ ° F −32 

⎝9⎠ ( ) 

⎛9⎞ ° F = ⎜ ×° C⎟+ 32 

⎝5⎠ ⎛5⎞ ° C = ⎜ ⎟( 

65° F−32) ⎝9⎠ ⎛5⎞ ° C = ⎜ ⎟( 

33 ) = ( 5 × 33 ) ÷ 9 

⎝9⎠ ° C = 165 ÷9 

° C = 18.3 

⎛9⎞ ° F = ⎜ ⎟( 

200 ° C) + 32 

⎝5⎠ ° F = [ ( 9 × 200 °C ) ÷ 5] + 32 

° F = [1800 ÷ 5] + 32 

° F = 360 + 32 

° 

F = 392 

8.2

Page 2 of 4 

1. For each of the problems below, show your calculations. Follow 

the steps from the examples on the previous page. 

a. What is the Celsius value for 212 °F? 

b. What is the Celsius value for 98.6 °F? 

c. What is the Celsius value for 40 °F? 

d. What is the Celsius value for 10 °F? 

e. What is the Fahrenheit value for 0 °C? 

f. What is the Fahrenheit value for 25 °C? 

g. What is the Fahrenheit value for 75 °C? 

2. The weatherman reports that today will reach a high of 45 °F. Your friend from Sweden asks what the 

temperature will be in degrees Celsius. What value would you report to your friend? 

3. Your parents order an oven from England. The temperature dial on the new oven is calibrated in degrees 

Celsius. If you need to bake a cake at 350 °F in the new oven, at what temperature should you set the dial? 

4. A German automobile’s engine temperature gauge reads in Celsius, not Fahrenheit. The engine temperature 

should not rise above about 225 °F. What is the corresponding Celsius temperature on this car’s gauge? 

5. Your grandmother in Ireland sends you her favorite cookie recipe. Her instructions say to bake the cookies at 

190 °C. To what Fahrenheit temperature would you set the oven to bake the cookies? 

6. A scientist wishes to generate a chemical reaction in his laboratory. The temperature values in his laboratory 

manual are given in degrees Celsius. However, his lab thermometers are calibrated in degrees Fahrenheit. If 

he needs to heat his reactants to 232 °C, what temperature will he need to monitor on his lab thermometers? 

7. You call a friend in Europe during the winter holidays and say that the temperature in Boston is 15 degrees. 

He replies that you must enjoy the warm weather. Explain his comment using your knowledge of the 

Fahrenheit and Celsius scales. To help you get started, fill in this table. What is 15 °F on the Celsius scale? 

What is 15°C on the Fahrenheit scale? 

°F f °C 

15 °F = 

= 15°C 

8. Challenge questions: 

a. A gas has a boiling point of –175 °C. At what Fahrenheit temperature would this gas boil? 

b. A chemist notices some silvery liquid on the floor in her lab. She wonders if someone accidentally 

broke a mercury thermometer, but did not thoroughly clean up the mess. She decides to find out if the 

silver stuff is really mercury. From her tests with the substance, she finds out that the melting point for 

the liquid is 35°F. A reference book says that the melting point for mercury is –38.87 °C. Is this 

substance mercury? Explain your answer and show all relevant calculations. 

8.2

Page 3 of 4 

Extension: the Kelvin temperature scale 

8.2 

For some scientific applications, a third temperature scale is used: the Kelvin scale. The Kelvin scale is 

calibrated so that raising the temperature one degree Kelvin raises it by the same amount as one degree Celsius. 

The difference between the scales is that 0 °C is the freezing point of water, while 0 K is much, much colder. On 

the Kelvin scale, 0K (degree symbols are not used for Kelvin values) represents absolute zero. Absolute zero is 

the temperature when the average kinetic energy of a perfect gas is zero—the molecules display no energy of 

motion. Absolute zero is equal to –273 °C, or –459 °F. When scientists are conducting research, they often obtain 

or report their temperature values in Celsius, and other scientists must convert these values into Kelvin for their 

own use, or vice versa. To convert Celsius values to their Kelvin equivalents, use the formula: 

K = °C + 273 

Water boils at a temperature of 100 °C. What would be the corresponding temperature for the Kelvin scale? 

K = °C + 273 

K = 100 °C + 273 

K = 373 

To convert Kelvin values to Celsius, you perform the opposite operation; subtract 273 from the Kelvin value to 

find the Celsius equivalent. 

A substance has a melting point of 625 K. At what Celsius temperature would this substance melt? 

°C = K + 273 

°C = 625 K −273 

°C = 352 

Although we rarely need to convert between Kelvin and Fahrenheit, use the following formulas to do so: 

⎛9⎞ °F = ⎜ × K ⎟−460 

⎝5⎠ 5 

K = (°F + 

460) 

9

Page 4 of 4 

1. Surface temperatures on the planet Mars range from –89 °C to –31 °C. Express this temperature 

range in Kelvin. 

2. The average surface temperature on Jupiter is about 165K. Express this temperature in degrees Celsius. 

3. The average surface temperature on Saturn is 134K. Express this temperature in degrees Celsius. 

4. The average surface temperature on the dwarf planet Pluto is 50K. Express this temperature in degrees 

Celsius. 

5. The Sun has several regions. The apparent surface that we can see from a distance is called the photosphere. 

Temperatures of the photosphere range from 5,000 °C to 8,000 °C. Express this temperature range in 

Kelvin. 

6. The chromosphere is a hot layer of plasma just above the photosphere. Chromosphere temperatures can 

reach 10,000 °C. Express this temperature in Kelvin. 

7. The outermost layer of the Sun’s atmosphere is called the corona. Its temperatures can reach over 

1,000,000 °C. Express this temperature in Kelvin. 

8. Nuclear fusion takes place in the center, or core, of the Sun. Temperatures there can reach 15,000,000 °C. 

Express this temperature in Kelvin. 

9. Challenge! Surface temperatures on Mercury can reach 660 °F. Express this temperature in Kelvin. 

10. Challenge! Surface temperatures on Venus, the hottest planet in our solar system, can reach 755K. Express 

this temperature in degrees Fahrenheit. 

8.2

Name: Date: 

8.3 Reading a Heating/Cooling Curve 

A heating curve shows how the temperature of a substance changes as 

heat is added at a constant rate. The heating curve at right shows what 

happens when heat is added at a constant rate to a beaker of ice. The flat 

spot on the graph, at zero degrees, shows that although heat was being 

added, the temperature did not rise while the solid ice was changing to 

liquid water. The heat energy was used to break the intermolecular 

forces between water molecules. Once all the ice changed to water, the 

temperature began to rise again. In this skill sheet, you will practice 

reading heating and cooling curves. 

The heating curve at right shows the temperature change in a 

sample of iron as heat is added at a constant rate. The sample 

starts out as a solid and ends as a gas. 

• Describe the phase change that occurred between points B 

and C on the graph. 

Solution: 

Between points B and C, the sample changed from solid to 

liquid. 

1. In the heating curve for iron, describe the phase change that 

occurred between points D and E on the graph. 

2. Explain why the temperature stayed constant between points D and E. 

3. What is the melting temperature of iron? 

4. What is the freezing temperature of iron? How do you know? 

5. What is the boiling temperature of iron? 

6. Compare the boiling temperatures of iron and water (water boils at 100°C). Which substance has stronger 

intermolecular forces? How do you know? 

8.3

Page 2 of 2 

The graph below shows a cooling curve for stearic acid. Stearic acid is a waxy solid at room 

temperature. It is derived from animal and vegetable fats and oils. It is used as an ingredient in soap, 

8.3 

candles, and cosmetics. In this activity, a sample of stearic acid was placed in a heat-resistant test tube 

and heated to 95 °C, at which point the stearic acid was completely liquefied. The test tube was placed in a 

beaker of ice water, and the temperature monitored until it reached 40 °C. Answer the following questions about 

the cooling curve: 

7. Between which two points on the graph did freezing occur? 

8. What is the freezing temperature of stearic acid? What is its melting temperature? 

9. Compare the melting temperature of stearic acid with the melting temperature of water. Which substance has 

stronger intermolecular forces? How do you know? 

10. Can a substance be cooled to a temperature below its freezing point? Use evidence from any of the graphs in 

this skill sheet to defend your answer.

Name: Date: 

9.1 Specific Heat 

Specific heat is the amount of thermal energy needed to raise the temperature of 1 gram of a substance 1 °C. 

The higher the specific heat, the more energy is required to cause a change in temperature. Substances with 

higher specific heats must lose more thermal energy to lower their temperature than substances with a low 

specific heat. Some sample specific heat values are presented in the table below: 

Material Specific Heat (J/kg °C) 

water (pure) 4,184 

aluminum 897 

silver 235 

oil 1,900 

concrete 880 

gold 129 

wood 1,700 

Water has the highest specific heat of the listed types of matter. This means that water is slower to heat but is 

also slower to lose heat. 

Using the table above, solve the following heat problems. 

1. If 100 joules of energy were applied to all of the substances listed in the table at the same time, which would 

have the greatest temperature change? Explain your answer. 

2. Which of the substances listed in the table would you choose as the best thermal insulator? A thermal 

insulator is a substance that requires a lot of heat energy to change its temperature. Explain your answer. 

3. Which substance—wood or silver—is the better thermal conductor? A thermal conductor is a material that 

requires very little heat energy to change its temperature. Explain your answer. 

4. Which has more thermal energy, 1 kg of aluminum at 20 °C or 1 kg of gold at 20 °C? 

5. How much heat in joules would you need to raise the temperature of 1 kg of water by 5 °C? 

6. How does the thermal energy of a large container of water compare to a small container of water at the same 

temperature? 

9.1

Name: Date: 

9.1 Using the Heat Equation 

You can solve real-world heat and temperature problems using the following equation: 

Below is a table that provides the specific heat of six everyday materials. 

Material Specific Heat (J/kg °C) Material Specific Heat (J/kg °C) 

water (pure) 4,184 concrete 880 

aluminum 897 gold 129 

silver 235 wood 1,700 

• How much heat does it take to raise the temperature of 10 kg of water by 10 °C? 

Solution: 

Find the specific heat of water from the table above: 4,184 J/kg °C. Plug the values into the equation. 

Thermal Energy (J) = 10 kg × 10 °C × 

4,184 J/kg • °C 

= 418,400 joules 

Use the specific heat table to answer the following questions. Don’t forget to show your work. 

1. How much heat does it take to raise the temperature of 0.10 kg of gold by 25 °C? 

2. How much heat does it take to raise the temperature of 0.10 kg of silver by 25 °C? 

3. How much heat does it take to raise the temperature of 0.10 kg of aluminum by 25 °C? 

4. Which one of the three materials above would cool down fastest after the heat was applied? Explain. 

5. A coffee maker heats 2 kg of water from 15 °C to 100 °C. How much thermal energy was required? 

6. The Sun warms a 100-kg slab of concrete from 20 °C to 25 °C. How much thermal energy did it absorb? 

7. 5,000 joules of thermal energy were applied to 1-kg aluminum bar. What was the temperature increase? 

8. In the 1920’s, many American homes did not have hot running water from the tap. Bath water was heated on 

the stove and poured into a basin. How much thermal energy would it take to heat 30 kg of water from 15 °C 

to a comfortable bath temperature of 50 °C? 

9.1

Name: Date: 

9.2 Heat Transfer 

Thermal energy flows from higher temperature to lower temperature. This process is called heat transfer. Heat 

transfer can occur three different ways: heat conduction, convection, and thermal radiation. Using section 9.2 of 

your student text as a guide, define each method of heat transfer. 

Heat conduction: 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

Convection: 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

Thermal radiation: 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

______________________________________________________________________________________ 

Read each scenario below. Then explain which type of heat transfer is described. Some scenarios involve more 

than one type of heat transfer. 

1. Mia places some frozen shrimp in a strainer and pours hot water over it so the shrimp will thaw faster. 

2. On a hot summer day, Juan can walk comfortably in bare feet on the concrete sidewalk, but finds that the 

asphalt road will burn the soles of his feet. 

3. A hawk soars upward, riding a thermal. 

4. An electric space heater warms an office. 

5. A mother duck sits on her eggs to keep them warm. 

6. A car parked in the sun reaches an interior temperature of 140°F in 40 minutes. 

7. Nick always adds milk to his coffee so that it’s not too hot to drink. 

8. A strong sea breeze makes a regatta (sailboat race) more exciting. 

9. Warm water piped under a marble floor makes the floor feel warm to bare feet. 

10. The warm water pipes under the marble floor heat the entire room. 

9.2

Name: Date: 

10.1 Measuring Mass with a Triple Beam Balance 

How do you find the mass of an object? 

Why can’t you use a bathroom scale to 

measure the mass of a paperclip? You could if 

you were finding the mass of a lot of them at 

one time! To find the mass of objects less than 

a kilogram you will need to use the triple beam 

balance. 

Parts of the triple beam balance 

Setting up and zeroing the balance 

The triple beam balance works like a see-saw. When the mass of your object is perfectly balanced by the counter 

masses on the beam, the pointer will rest at 0. Add up the readings on the three beams to find the mass of your 

object. The unit of measure for this triple beam balance is grams. 

1. Place the balance on a level surface. 

2. Clean any objects or dust off the pan. 

Materials 

• Triple beam balance 

• Small objects 

• Mass set (optional) 

• Beaker 

3. Move all counter masses to 0. The pointer should rest at 0. Use the adjustment screw to adjust the pointer to 

0, if necessary. When the pointer rests at 0 with no objects on the pan, the balance is said to be zeroed.

Page 2 of 3 

Finding a known mass 

You can check that the triple beam balance is working correctly by using a mass set. Your teacher will 

provide the correct mass value for these objects. 

1. After zeroing the balance, place an object with a known mass on the pan. 

2. Move the counter masses to the right one at a time from largest to smallest. When the pointer is resting at 0 

the numbers under the three counter masses should add up to the known mass. 

3. If the pointer is above or below 0, recheck the balance set up. Recheck the position of the counter masses. 

Counter masses must be properly seated in a groove. Check with your teacher to make sure you are getting 

the correct mass before finding the mass an unknown object. 

Finding the mass of an unknown object 

1. After zeroing the balance, place an object with an unknown mass on the pan. Do not place hot objects or 

chemicals directly on the pan 

2. Move the largest counter mass first. Place it in the first notch after zero. Wait until the pointer stops moving. 

If the pointer is above 0, move the counter mass to the next notch. Continue to move the counter mass to the 

right, one notch at a time until the pointer is slightly above 0. Go to step 3. If the pointer is below 0, move the 

counter mass back one notch. When the pointer rests at 0, you do not need to move any more counter 

masses. 

3. Move the next largest counter mass from 0 to the first notch. Watch to see where the pointer rests. If it rests 

above 0, move the counter mass to the next notch. Repeat until the point rests at 0, or slightly above. If the 

pointer is slightly above 0, go to step 4. 

4. Move the smallest counter mass from 0 to the position on the beam where the pointer rests at 0. 

5. Add the masses from the three beams to get the mass of the unknown object. You should be able to record a 

number for the hundreds place, the tens place, the ones place, and the tenths place and the hundredths place. 

The hundredths place can be read to 0.00 or 0.05. You may have zeros in your answer.

Page 3 of 3 

Reading the balance correctly 

Look at the picture above. To find the mass of the object, locate the counter mass on each beam. Read the 

numbers directly below each counter mass. You can read the smallest mass to 0.05 grams. Write down the three 

numbers. Add them together. Report your answer in grams. Does your answer agree with others? If not, check 

your mass values from each beam to find your mistake. 

Finding the mass of an object in a container 

To measure the mass of a liquid or powder you will need an empty container on the pan to hold the sample. You 

must find the mass of the empty container first. After you place the object in the container and find the total mass, 

you can subtract the container’s mass from the total to find the object’s mass. 

1. After zeroing the balance, place a beaker on the pan. 

2. Follow directions for finding the mass of an unknown object. Record the mass of the beaker. 

3. Place a small object in the beaker. 

4. Move the counter masses to the right, largest to smallest, to find the total mass. 

5. Subtract the beaker’s mass from the total mass. This is the mass of your object in grams.

Name: Date: 

10.1 Measuring Volume 

How do you find the volume of an irregular object? 

It’s easy to find the volume of a shoebox or a 

basketball. You just take a few measurements, 

plug the numbers into a math formula, and you 

have figured it out. But what if you want to find 

the volume of a bumpy rock, or an acorn, or a 

house key? There aren’t any simple math 

formulas to help you out. However, there’s an 

easy way to find the volume of an irregular 

object, as long the object is waterproof! 

Setting up the displacement tank 

Materials 

• Displacement tank 

• Water source 

• Disposable cup 

• Beaker 

• Graduated cylinder 

• Sponges or paper towel 

• Object to be measured 

Set the displacement tank on a level surface. Place a disposable cup 

under the tank’s spout. Carefully fill the tank until the water begins to 

drip out of the spout. When the water stops flowing, discard the water 

collected in the disposable cup. Set the cup aside and place a beaker 

under the spout. 


a. What do you think will happen when you place an object into the 

tank? 

b. Which object would cause more water to come out of the spout, an acorn or a fist-sized rock? 

c. Why are we interested in how much water comes out of the spout?

Page 2 of 2 

d. Explain how the displacement tank measures volume. 

Measuring volume with the displacement tank 

1. Gently place a waterproof object into the displacement tank. It is important to avoid splashing the water or 

creating a wave that causes extra water to flow out of the spout. It may take a little practice to master this 

step. 

2. When the water stops flowing out of the spout, it can be poured from the beaker into a graduated cylinder for 

precise measurement. The volume of the water displaced is equal to the object’s volume. 

Note: Occasionally, when a small object is placed in the tank, no water will flow out. This happens because 

an air bubble has formed in the spout. Simply tap the spout with a pencil to release the air bubble. 

3. If you wish to measure the volume of another object, don’t forget to refill the tank with water first!

Name: Date: 

10.1 Calculating Volume 

How do you find the volume of a three dimensional shape? 

Volume is the amount of space an object takes 

up. If you know the dimensions of a solid object, 

you can find the object's volume. A two 

dimensional shape has length and width. A 

three dimensional object has length, width, and 

height. This investigation will give you practice 

finding volume for different solid objects. 

Calculating volume of a cube 

A cube is a geometric solid that has length, width and height. If you 

measure the sides of a cube, you will find that all the edges have the 

same measurement. The volume of a cube is found by multiplying the 

length times width times height. In the picture each side is 

4 centimeters so the problem looks like this: 

Example: 

V= l × w × h 

Volume = 4 centimeters × 4 centimeters × 4 centimeters = 64 centimeters 3 


a. What are the units for volume in the example above? 

b. In the example above, if the edge of the cube is 4 inches, what will the volume be? Give the units. 

c. How is finding volume different from finding area? 

Materials 

• Pencil 


d. If you had cubes with a length of 1 centimeter, how many would you need to build the cube in the picture above? 

Calculating volume of a rectangular prism 

Rectangular prisms are like cubes, except not all of the sides are 

equal. A shoebox is a rectangular prism. You can find the 

volume of a rectangular prism using the same formula given 

above (V= l × w × h.) 

Another way to say it is to multiply the area of the base times the 

height. 

1. Find the area of the base for the rectangular prism pictured 

above. 

2. Multiply the area of the base times the height. Record the volume of the rectangular prism. 

3. PRACTICE: Find the volume for a rectangular prism with a height 6 cm, length 5 cm, and width 3 cm. Be 

sure to include the units in all of your answers.

Page 2 of 3 

Calculating volume of a triangular prism 

Triangular prisms have three sides and two triangular 

bases. The volume of the triangular prism is found by 

multiplying the area of the base times the height. The 

base is a triangle. 

1. Find the area of the base by solving for the area of 

the triangle: B = 1 / 2 × l × w. 

2. Find the volume by multiplying the area of the base 

times the height of the prism: 

V= B × h. Record the volume of the triangular prism 

shown above. 

3. PRACTICE: Find the volume of the triangular prism with a height 10 cm, triangular base width 4 cm, and 

triangular base length 5 cm. 

Calculating volume of a cylinder 

A soup can is a cylinder. A cylinder has two circular bases and a 

round surface. The volume of the cylinder is found by multiplying 

the area of the base times the height. The base is a circle. 

1. Find the area of the base by solving for the area of a 

circle: A = π×r 2 . 

2. Find the volume by multiplying the area of the base times the 

height of the cylinder: V = A × h. Record the volume of the 

cylinder shown above. 

3. PRACTICE: Find the volume of the cylinder with height 8 cm 

and radius 4 cm. 

Calculating volume of a cone 

An ice cream cone really is a cone! A cone has height and a circular 

base. The volume of the cone is found by multiplying 1 / 3 times the 

area of the base times the height. 

1. Find the area of the base by solving for the area of a circle: 

A = π×r2 . 

2. Find the volume by multiplying 1 / 3 times the area of the base 

times the height: 

V = 1 / 3 × A × h. Record the volume of the cone shown above. 

3. PRACTICE: Find the volume of the cone with height 8 cm and 

radius 4 cm. Contrast your answer with the volume you found for the cylinder with the same dimensions. 

What is the difference in volume? Does this make sense?

Page 3 of 3 

Calculating the volume of a rectangular pyramid 

A pyramid looks like a cone. It has height and a rectangular base. The 

volume of the rectangular pyramid is found by multiplying 1 / 3 times 

the area of the base times the height. 

1. Find the area of the base by multiplying the length times the 

width: A = l × w. 

2. Find the volume by multiplying 1 / 3 times the area of the base 

times the height: 

V = 1 / 3 × A × h. Record the volume of the rectangular pyramid 

shown above. 

3. PRACTICE: Find the volume of a rectangular pyramid with 

height 10 cm and width 4 cm and length 5 cm. 

4. EXTRA CHALLENGE: If a rectangular pyramid had a height of 8 cm and a width of 4 cm, what length 

would it need to have to give the same volume as the cone in practice question 3 above? 

Calculating volume of a triangular pyramid 

A triangular pyramid is like a rectangular pyramid, but its base is 

a triangle. Find the area of the base first. Then calculate the 

volume by multiplying 1 / 3 times the area of the base times the 

height. 

1. Find the area of the base by solving for the area of a triangle: 

B = 1 / 2 × l × w. 

2. Find the volume by multiplying 1 / 3 times the area of the 

base times the height: 

V= 1 / 3 × A × h. Find the volume of the triangular pyramid 

shown above. 

3. PRACTICE: Find the volume of the triangular pyramid with 

height 10 cm and whose base has width 6 cm and length 

5cm. 

Calculating volume of a sphere 

To find the volume of a sphere, you only need to know one dimension 

about the sphere, its radius. 

1. Find the volume of a sphere: V = 4 / 3πr 3 . Find the volume for the 

sphere shown above. 

2. PRACTICE: Find the volume for a sphere with radius 2 cm. 

3. EXTRA CHALLENGE: Find the volume for a sphere with 

diameter 10 cm.

Name: Date: 

10.1 Density 

The density of a substance does not depend on its size or shape. As 

long as a substance is homogeneous, the density will be the same. 

This means that a steel nail has the same density as a cube of steel or a 

steel girder used to build a bridge. 

The formula for density is: 

density 

------------------mass 

volume 

One milliliter takes up the same amount of space as one cubic 

centimeter. Therefore, density can be expressed in units of g/mL or 

g/cm 3 . Liquid volumes are most commonly expressed in milliliters, 

while volumes of solids are usually expressed in cubic centimeters. 

Density can also be expressed in units of kilograms per cubic meter (kg/m 3 ). 

If you know the density of a substance and the volume of a sample, you can calculate the mass of the sample. To 

do this, rearrange the equation above to find mass: volume × density = mass 

If you know the density of a substance and the mass of a sample, you can find the volume of the sample. This 

time, you will rearrange the density equation to find volume: 

mass 

volume = ---------------density 

Example 1: What is the density of a block of aluminum with a volume of 30.0 cm3 and a mass of 81.0 grams? 

density 

81.0 g 

30.0 cm3 ---------------------- 

2.70 g 

cm3 = = -------------- 

Answer: The density of aluminum is 2.70 g/cm 3 . 

Example 2: What is the mass of an iron horseshoe with a volume of 89.0 cm3 ? The density of iron is 7.90 g/cm3 . 

mass 89.0cm 

Answer: The mass of the horseshoe is 703 grams. 

3 7.90 g 

cm3 = × ---------- = 703 grams 

Example 3: What is the volume of a 525-gram block of lead? The density of lead is 11.3 g/cm3 . 

volume 

525 g 

11.3 g 

cm3 --------------------- 

---------- 

46.5 cm3 = = 

Answer: The volume of the block is 46.5 cm 3 . 

= 

10.1

Page 2 of 2 

Answer the following density questions. Report your answers using the correct number of significant 

digits. 

1. A solid rubber stopper has a mass of 33.0 grams and a volume of 30.0 cm 3 . What is the density of rubber? 

2. A chunk of paraffin (wax) has a mass of 50.4 grams and a volume of 57.9 cm 3 . What is its density? 

3. A marble statue has a mass of 6,200 grams and a volume of 2,296 cm 3 . What is the density of marble? 

4. The density of ice is 0.92 g/cm 3 . An ice sculptor orders a 1.0-m 3 block of ice. What is the mass of the block? 

Hint: 1 m 3 = 1,000,000 cm 3 . Give your answer in grams and kilograms. 

5. What is the mass of a pure platinum disk with a volume of 113 cm 3 ? The density of platinum is 21.4 g/cm 3 . 

Give your answer in grams and kilograms. 

6. The density of seawater is 1.025 g/mL. What is the mass of 1.000 liter of seawater in grams and in 

kilograms? (Hint: 1 liter = 1,000 mL) 

7. The density of cork is 0.24 g/cm 3 . What is the volume of a 288-gram piece of cork? 

8. The density of gold is 19.3 g/cm 3 . What is the volume of a 575-gram bar of pure gold? 

9. The density of mercury is 13.6 g/mL. What is the volume of a 155-gram sample of mercury? 

10. Recycling centers use density to help sort and identify different types of plastics so that they can be properly 

recycled. The table below shows common types of plastics, their recycling code, and density. Use the table 

to solve problems 10a–d. 

Plastic name Common uses Recycling code Density (g/cm 3 ) Density (kg/m 3 ) 

PETE plastic soda bottles 1 1.38–1.39 1,380–1,390 

HDPE milk cartons 2 0.95–0.97 950–970 

PVC plumbing pipe 3 1.15–1.35 1,150–1,350 

LDPE trash can liners 4 0.92–0.94 920–940 

PP yogurt containers 5 0.90–0.91 900–910 

PS cd “jewel cases” 6 1.05–1.07 1,050–1,070 

a. A recycling center has a 0.125 m 3 box filled with one type of plastic. When empty, the box had a mass 

of 0.755 kilograms. The full box has a mass of 120.8 kilograms. What is the density of the plastic? What 

type of plastic is in the box? 

b. A truckload of plastic soda bottles was finely shredded at a recycling center. The plastic shreds were 

placed into 55-liter drums. What is the mass of the plastic shreds inside one of the drums? 

Hint: 55 liters = 55,000 milliliters = 55,000 cm 3 . 

c. A recycling center has 100. kilograms of shredded plastic yogurt containers. What volume is needed to 

hold this amount of shredded plastic? How many 10.-liter (10,000 mL) containers do they need to hold 

all of this plastic? Hint: 1 m 3 = 1,000,000 mL. 

d. A solid will float in a liquid if it is less dense than the liquid, and sink if it is more dense than the liquid. 

If the density of seawater is 1.025 g/mL, which types of plastics would definitely float in seawater? 

10.1

Name: Date: 

10.3 Pressure in Fluids 

Have you ever wondered how a 1,500-kilogram car is raised off the ground in a mechanic’s shop? A hydraulic 

lift does the trick. All hydraulic machines operate on the basis of Pascal’s principle, which states that the pressure 

applied to an incompressible fluid in a closed container is transmitted equally in all parts of the fluid. 

In the diagram above, a piston at the top of the small tube pushes down on the fluid. This input force generates a 

certain amount of pressure, which can be calculated using the formula: 

That pressure stays the same throughout the fluid, so it remains the same in the large cylinder. Since the large 

cylinder has more area, the output force generated by the large cylinder is greater. The output force exerted by the 

piston at the top of the large cylinder can be calculated using the formula: 

You can see that the small input force created a large output force. But there’s a price: The small piston must be 

pushed a greater distance than the large piston moves. Work output (output force × output distance) can never be 

greater than work input (input force × input distance). 

• A 50.-newton force is applied to a small piston with an area of 0.0025 m 2 . What pressure, in pascals, will be 

transmitted in the hydraulic system? 

Solution: 

• The area of the large cylinder’s piston in this hydraulic system is 2.5 m 2 . What is the output force? 

Solution: 

Pressure 

Pressure 

= 

Force 

-------------- 

Area 

Force = Pressure × Area 

= 

Force 

-------------- 

Area 

= 

50. N 

0.0025 m 2 

------------------------- = 20000 Pa 

Force Pressure × Area = 20000 Pa 2.5 m 2 

= 

× = 50000 N 

10.3

Page 2 of 2 

1. In a hydraulic system, a 100.-newton force is applied to a small piston with an area of 0.0020 m 2 . 

What pressure, in pascals, will be transmitted in the hydraulic system? 

2. The area of the large cylinder’s piston in this hydraulic system is 3.14 m 2 . What is the output force? 

3. An engineer wishes to design a hydraulic system that will transmit a pressure of 10,000 pascals using a force 

of 15 newtons. How large an area should the input piston have? 

4. This hydraulic system should produce an output force of 50,000 newtons. How large an area should the 

output piston have? 

5. Another engineer is running a series of experiments with hydraulic systems. If she doubles the area of the 

input piston, what happens to the amount of pressure transmitted by the system? 

6. If all other variables remain unchanged, what happens to the output force when the area of the input piston is 

doubled? 

7. If the small piston in the hydraulic system described in problems 1 and 2 is moved a distance of 2 meters, 

will the large piston also move 2 meters? Explain why or why not. 

8. A 540-newton woman can make dents in a hardwood floor wearing high-heeled shoes, yet if she wears 

snowshoes, she can step effortlessly over soft snow without sinking in. Explain why, using what you know 

about pressure, force, and area. 

10.3

Name: Date: 

10.3 Boyle’s Law 

The relationship between the volume of a gas 

and the pressure of a gas, at a constant 

temperature, is known as Boyle’s law. The 

equation for Boyle’s law is shown at right. 

Units for pressure include: atmospheres 

(atm), pascals (Pa), or kilopascals (kPa). 

Units for volume include: cubic centimeters 

(cm 3 ), cubic meters (m 3 ), or liters. 

A kit used to fix flat tires consists of an aerosol can containing compressed air and a patch to seal the hole in the 

tire. Suppose 10.0 L of air at atmospheric pressure (101.3 kilopascals, or kPa) is compressed into a 1.0-L aerosol 

can. What is the pressure of the compressed air in the can? 

Looking for 

Pressure of compressed air in a can (P2) Given 

P1 = 101.3 kPa; V1 = 10.0 liters; V2 = 1.0 liters 

Relationship 

Use Boyle’s Law to solve for P2. Divide each side by V2 to isolate P2 on one side of the equation. 

P V 

P 

1 1 

2 

= 

------------- 

V 

2 

Solution 

The pressure inside the aerosol can is 

1,013 kPa. 

1. The air inside a tire pump occupies a volume of 130. cm 3 at a pressure of one atmosphere. If the volume 

decreases to 40.0 cm 3 , what is the pressure, in atmospheres, inside the pump? 

2. A gas occupies a volume of 20. m 3 at 9,000. Pa. If the pressure is lowered to 5,000. Pa, what volume will the 

gas occupy? 

3. You pump 25.0 L of air at atmospheric pressure (101.3 kPa) into a soccer ball that has a volume of 4.50 L. 

What is the pressure inside the soccer ball if the temperature does not change? 

4. Hyperbaric oxygen chambers (HBO) are used to treat divers with decompression sickness. As pressure 

increases inside the HBO, more oxygen is forced into the bloodstream of the patient inside the chamber. To 

work properly, the pressure inside the chamber should be three times greater than atmospheric pressure 

(101.3 kPa). What volume of oxygen, held at atmospheric pressure, will need to be pumped into a 190.-L 

HBO chamber to make the pressure inside three times greater than atmospheric pressure? 

5. A 12.5-liter scuba tank holds oxygen at a pressure of 202.6 kPa. What is the original volume of oxygen at 

101.3 kPa that is required to fill the scuba tank? 

P 2 

101.3 kPa × 10.0 L 

= --------------------------------------------- = 1,013 kPa 

1.0 L 

10.3

Name: Date: 

10.4 Buoyancy 

When an object is placed in a fluid (liquid or gas), the fluid exerts an upward force upon the object. This force is 

called a buoyant force. 

At the same time, there is an attractive force between the object and Earth—the force of gravity. It acts as a 

downward force. You can compare the two forces to determine whether the object floats or sinks in the fluid. 

Buoyant force > Gravitational force Buoyant force < Gravitational force 

Object floats Object sinks 

Example 1: A 13-N object is placed in a container of fluid. If the fluid exerts a 60-N buoyant (upward) force on 

the object, will the object float or sink? 

Answer: Float. The upward buoyant force (60 N) is greater than the weight of the object (13 N). 

Example 2: The rock weighs 2.25 N when suspended in air. In water, it 

appears to weigh only 1.8 N. Why? 

Answer: The water exerts a buoyant force on the rock. This buoyant force 

equals the difference between the rock’s weight in air and its apparent weight 

in water. 

2.25 N – 1.8 N = 

0.45 N 

The water exerts a buoyant force of 0.45 newtons on the rock. 

1. A 4.5-N object is placed in a tank of water. If the water exerts a force of 4.0 N on the object, will the object 

sink or float? 

2. The same 4.5-N object is placed in a tank of glycerin. If the glycerin exerts a force of 5.0 N on the object, 

will the object sink or float? 

3. You suspend a brass ring from a spring scale. Its weight is 0.83 N while it is suspended in air. Next, you 

immerse the ring in a container of light corn syrup. The ring appears to weigh 0.71 N. What is the buoyant 

force acting on the ring in the light corn syrup? 

4. You wash the brass ring (from question 3) and then suspend it in a container of vegetable oil. The ring 

appears to weigh 0.73 N. What is the buoyant force acting on the ring? 

5. Which has greater buoyant force, light corn syrup or the vegetable oil? Why do you think this is so? 

6. A cube of gold weighs 1.89 N when suspended in air from a spring scale. When suspended in molasses, it 

appears to weigh 1.76 N. What is the buoyant force acting on the cube? 

7. Do you think the buoyant force would be greater or smaller if the gold cube were suspended in water? 

Explain your answer. 

10.4

Name: Date: 

10.4 Charles’s Law 

Charless law shows a direct relationship between the volume of a gas and the temperature of a gas when the 

temperature is given in the Kelvin scale. The Charles’s law equation is below. 

Converting from degrees Celsius to Kelvin is easy—you add 273 to the Celsius temperature. To convert from 

Kelvins to degrees Celsius, you subtract 273 from the Kelvin temperature. 

A truck tire holds 25.0 liters of air at 25 °C. If the temperature drops to 0 °C, and the pressure remains constant, 

what will be the new volume of the tire? 

Looking for 

The new volume of the tire (V2) Given 

V1 = 25.0 liters; T1 = 25 °C; T2 = 0 °C 

Relationships 

Use Charles’ Law to solve for V2. Multiply each side 

by T2 to isolate V2 on one side of the equation. 

V T 

V = 

------------- 

1 2 

2 T 

1 

Convert temperature values in Celsius degrees to 

Kelvin: T Kelvin = T Celsius + 273 

Solution 

T 1 = 25 °C + 273 = 298 

T 2 = 0 °C + 273 = 273 

The new volume inside the tire is 23.0 liters. 

1. If a truck tire holds 25.0 liters of air at 25.0 °C, what is the new volume of air in the tire if the temperature 

increases to 30.0 °C? 

2. A balloon holds 20.0 liters of helium at 10.0 °C. If the temperature increases to 50.0 °C, and the pressure 

does not change, what is the new volume of the balloon? 

3. Use Charles’ Law to fill in the following table with the correct values. Pay attention to the temperature units. 

V1 T1 V2 T2 a. 840 K 1,070 mL 147 K 

b. 3250 mL 475 °C 50 °C 

c. 10 L 15 L 50 °C 

V 2 

25.0 L × 273 

= ------------------------------ = 23.0 L 

298 

10.4

Name: Date: 

10.4 Pressure-Temperature Relationship 

The pressure-temperature relationship shows a 

direct relationship between the pressure of a gas 

and its temperature when the temperature is given 

in the Kelvin scale. Another name for this 

relationship is the Gay-Lussac Law. The pressuretemperature 

equation is shown at right. 

Converting from degrees Celsius to Kelvin is easy 

—you add 273 to the Celsius temperature. To 

convert from Kelvins to degrees Celsius, you 

subtract 273 from the Kelvin temperature. 

A constant volume of gas is heated from 25.0°C to 100°C. If the gas pressure starts at 1.00 atmosphere, what is 

the final pressure of this gas? 

Looking for 

The new pressure of the gas (P2) Given 

T1 = 25 °C; P1 = 1 atm; T2 = 100 °C 

Relationships 

Use pressure-temperature relation to solve for P2. Multiply 

each side by T2 to isolate P2 on one side of the equation. 

P 

1 

T 

2 

P 

2 

= 

------------- 

T 

1 

Convert temperature values in Celsius degrees to Kelvin: 

T Kelvin = T Celsius + 273 

Solution 

T 1 = 25 °C + 273 = 298 

T 2 = 100 °C + 373 = 313 

The new pressure of the volume of gas 

is 1.25 atmospheres. 

1. At 400. K, a volume of gas has a pressure of 0.40 atmospheres. What is the pressure of this gas at 273 K? 

2. What is the temperature of the volume of gas (starting at 400. K with a pressure of 0.4 atmospheres), when 

the pressure increases to 1 atmosphere? 

3. Use the pressure-temperature relationship to fill in the following table with the correct values. Pay attention 

to the temperature units. 

P1 T1 P2 T2 a. 30.0 atm –100 °C 500 °C 

b. 15.0 atm 25.0 °C 18.0 atm 

c. 5.00 atm 3.00 atm 293 K 

P 2 

1 atm × 373 

= ---------------------------- = 1.25 atm 

298 

10.4

Name: Date: 

10.4 Archimedes 

10.4 

Archimedes was a Greek mathematician who specialized in geometry. He figured out the value of pi 

and the volume of a sphere, and has been called “the father of integral calculus.” During his lifetime, he was 

famous for using compound pulleys and levers to invent war machines that successfully held off an attack on his 

city for three years. Today he is best known for Archimedes’ principle, which was the first explanation of how 

buoyancy works. 

Archimedes’ screw 

Archimedes was born in 

Syracuse, on Sicily (then an 

independent Greek city-state), 

in 287 B.C. His letters suggest 

that he studied in Alexandria, 

Egypt, as a young man. 

Historians believe it was there 

that he invented a device for 

raising water by means of a 

rotating screw or spirally bent 

tube within an inclined hollow 

cylinder. The device known as Archimedes’ screw is 

still used in many parts of the world. 

“Eureka!” 

A famous Greek legend says that King Hieron II of 

Syracuse asked Archimedes to figure out if his new 

crown was pure gold or if the craftsman had mixed 

some less expensive silver into it. Archimedes had to 

determine the answer without destroying the crown. 

He thought about it for days and then, as he lowered 

himself into a bath, the method for figuring it out 

struck him. The legend says Archimedes ran through 

the streets, shouting “Eureka!”—meaning “I have 

found it.” 

A massive problem 

Archimedes realized that if 

he had equal masses of gold 

and silver, the denser gold 

would have a smaller 

volume. Therefore, the gold 

would displace less water 

than the silver when 

submerged. 

Archimedes found the mass 

of the crown and then made 

a bar of pure gold with the 

same mass. He submerged 

the gold bar and measured the volume of water it 

displaced. Next, he submerged the crown. He found 

the crown displaced more water than the gold bar had 

and, therefore, could not be pure gold. The gold had 

been mixed with a less dense material. Archimedes 

had confirmed the king’s doubts. 

Why do things float? 

Archimedes wrote a treatise titled On Floating Bodies, 

further exploring density and buoyancy. He explained 

that an object immersed in a fluid is pushed upward by 

a force equal to the weight of the fluid displaced by the 

object. Therefore, if an object weighs more than the 

fluid it displaces, it will sink. If it weighs less than the 

fluid it displaces, it will float. This statement is known 

as Archimedes’ principle. Although we commonly 

assume the fluid is water, the statement holds true for 

any fluid, whether liquid or gas. A helium balloon 

floats because the air it displaces weighs more than the 

balloon filled with lightweight gas. 

Cylinders, circles, and exponents 

Archimedes wrote several other treatises, including 

“On the Sphere and the Cylinder,” “On the 

Measurement of the Circle,” “On Spirals,” and “The 

Sand Reckoner.” In this last treatise, he devised a 

system of exponents that allowed him to represent 

large numbers on paper—up to 8 × 10 63 in modern 

scientific notation. This was large enough, he said, to 

count the grains of sand that would be needed to fill 

the universe. This paper is even more remarkable for 

its astronomical calculations than for its new 

mathematics. Archimedes first had to figure out the 

size of the universe in order to estimate the amount of 

sand needed to fill it. He based his size calculations on 

the writings of three astronomers (one of them was his 

father). While his estimate is considered too small by 

today’s standard, it was much, much larger than 

anyone had previously suggested. Archimedes was the 

first to think on an “astronomical scale.” 

Archimedes was killed by a Roman soldier during an 

invasion of Syracuse in 212 B.C.

Page 2 of 2 


1. The boldface words in the article are defined in the glossary of your textbook. Look them up and 

then explain the meaning of each in your own words. 

2. Imagine you are Archimedes and have to write your resume for a job. Describe yourself in a brief paragraph. 

Be sure to include in the paragraph your skills and the jobs you are capable of doing. 

3. What was Archimedes’ treatise “The Sand Reckoner” about? 

4. Why does a balloon filled with helium float in air, but a balloon filled with air from your lungs sink? 

5. Research one of Archimedes’ inventions and create a poster that shows how the device worked. 

10.4

Name: Date: 

10.4 Narcís Monturiol 

10.4 

Monturiol, a visionary and peaceful revolutionary, wanted to improve the social and economic lives of 

his countrymen. Moved by the suffering of coral divers due to their extremely dangerous working conditions, 

Monturiol built a submarine to transport the divers to the reefs. He hoped that in time, his invention would also 

help people understand the ocean world. 

Birth of a Spanish inventor 

Narcís Monturiol was born 

on September 28, 1819, in 

Figueres, Catalonia, a 

region of northeastern 

Spain. Monturiol’s father 

was a cooper—which 

means that he handcrafted 

wooden barrels that held 

wine, oil, and milk. Narcís 

was one of five children. At 

an early age he showed an 

interest in design and 

invention. When he was ten, he created a realistic 

model of a wooden clock. 

His mother wanted Narcís to become a priest, but he 

earned a law degree instead. He never practiced law, 

however. Instead, he became a self-taught engineer. 

Monturiol was active politically. He supported 

socialism, communism, and the ideal of a utopia 

where everyone lived together in harmony. He turned 

to science with the hope of creating that utopia. 

The perils of coral diving 

Monturiol was concerned about the danger involved in 

the work of Spanish coral fishermen. A diver, holding 

his breath for several minutes, dove nearly 20 meters 

beneath the ocean surface to retrieve valuable pieces 

of coral. The divers risked drowning, injuries from 

rocks and coral, and possible shark attacks. 

In 1857, Monturiol formed a company to design and 

build a submarine. His goal was to develop a vessel to 

help coral divers with their physical work and to 

lessen the risk involved. 

Monturiol was not the first to build a submarine. 

Historical records show that Aristotle, Renaissance 

period inventors, and others had attempted to build 

submarines. These models were often created for 

warfare. Most early submarines were unsuccessful and 

dangerous. 

Ictineo I 

Monturiol’s first submarine, Ictineo I, made its first dive 

in 1859. The name Ictineo is derived from Greek, and is 

translated “fish ship.” During its initial dive, Ictineo I hit 

underwater pilings. Repairing what he could, Monturiol 

sent Ictineo I on its second dive within a few hours. 

Monturiol’s seven-meter submarine had a spherical inner 

hull built to withstand water pressure, and an elliptical 

(egg-shaped) outer hull for ease of movement. Between 

the two hulls were tanks that stored and released water to 

control the submarine’s depth. Oxygen tanks were also 

stored in this space. The submarine was powered by four 

men turning the propeller by hand. 

Ictineo I was equipped with a ventilator, two sets of 

propellers, and several portholes. The submarine had 

the ability to retrieve objects and was equipped with a 

back-up system to raise it to the surface in an 

emergency. 

Ictineo I made nearly 20 dives that first year, to a 

depth of 20 meters. The submarine eventually stayed 

underwater for nearly two hours. 

Ictineo II 

Monturiol created a second and improved model 

called Ictineo II. Rather than relying on manpower, the 

Ictineo II had a steam engine. These engines were 

traditionally powered by an open flame. Monturiol 

created a submarine-safe alternative to power the 

engine using a chemical reaction. The open flame 

would have removed oxygen, but the chemical 

reaction added oxygen to the cabin instead. 

The Ictineo II was 17 meters long, had two engines, 

dove to depths of nearly 30 meters, had many portholes, 

and remained underwater for almost seven hours. 

Unfortunately, Monturiol ran out of funds and was 

forced to sell his submarine for scrap. Although he 

didn’t receive much credit for his inventions during 

his lifetime, he is now recognized as an important 

contributor to submarine development. Monturiol died 

in 1885.

Page 2 of 2 


1. What moved Monturiol to create a submarine? 

2. Identify key features of the Ictineo I and II. 

3. Research: Where are model replicas of Ictineo I and II located? 

4. Research: What happed to Monturiol’s Ictineo I? 

5. Research: Name three things Monturiol invented in addition to the submarine. 

6. Research: How did Spain honor Monturiol in 1987? 

7. Research: What is the Narcís Monturiol medal? 

10.4

Name: Date: 

10.4 Archimedes’ Principle 

More than 2,000 years ago, Archimedes discovered the relationship between buoyant force and how much fluid 

is displaced by an object. Archimedes’ principle states: 

The buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object. 

We can practice figuring out the buoyant force using a beach ball and a big tub of water. Our beach ball has a 

volume of 14,130 cm 3 . The weight of the beach ball in air is 1.5 N. 

If you put the beach ball into the water and don’t push down on it, you’ll see that 

the beach ball floats on top of the water by itself. Only a small part of the beach 

ball is underwater. Measuring the volume of the beach ball that is under water, we 

find it is 153 cm 3 . Knowing that 1 cm 3 of water has a mass of 1 g, you can 

calculate the weight of the water displaced by the beach ball. 

153 cm 3 of water = 153 grams = 0.153 kg 

weight = mass × force of gravity per kg = (0.153 kg) × 9.8 N/kg = 1.5 N 

According to Archimedes principle, the buoyant force acting on the beach ball equals the weight of the water 

displaced by the beach ball. Since the beach ball is floating in equilibrium, the weight of the ball pushing down 

must equal the buoyant force pushing up on the ball. We just showed this to be true for our beach ball. 

Have you ever tried to hold a beach ball underwater? It takes a lot 

of effort! That is because as you submerge more of the beach ball, 

the more the buoyant force acting on the ball pushes it up. Let’s 

calculate the buoyant force on our beach ball if we push it all the 

way under the water. Completely submerged, the beach ball 

displaces 14,130 cm 3 of water. Archimedes principle tells us that 

the buoyant force on the ball is equal to the weight of that water: 

14,130 cm 3 of water = 14,130 grams = 14.13 kg 

weight = mass × force of gravity per kg = (14.13 kg) × 9.8 N/kg = 138 N 

If the buoyant force is pushing up with 138 N, and the weight of the ball is only 1.5 N, your hand pushing down 

on the ball supplies the rest of the force, 136.5 N. 

• A 10-cm3 block of lead weighs 1.1 N. The lead is placed in a tank of water. One cm3 of water weighs 0.0098 

N. What is the buoyant force on the block of lead? 

Solution: 

The lead displaces 10 cm3 of water. 

buoyant force = weight of water displaced 

10 cm 3 of water × 0.0098 N/cm3 = 0.098 N 

10.4

Page 2 of 2 

1. A block of gold and a block of wood both have the same volume. If they are both submerged in 

water, which has the greater buoyant force acting on it? 

2. A 100-cm3 block of lead that weighs 11 N is carefully submerged in water. One cm3 of water weighs 

0.0098 N. 

a. What volume of water does the lead displace? 

b. How much does that volume of water weigh? 

c. What is the buoyant force on the lead? 

d. Will the lead block sink or float in the water? 

3. The same 100-cm 3 lead block is carefully submerged in a container of mercury. One cm3 of mercury weighs 

0.13 N. 

a. What volume of mercury is displaced? 

b. How much does that volume of mercury weigh? 

c. What is the buoyant force on the lead? 

d. Will the lead block sink or float in the mercury? 

4. According to problems 2 and 3, does an object’s density have anything to do with whether or not it will float 

in a particular liquid? Justify your answer. 

5. Based on the table of densities, explain whether the object would float or sink in the following situations: 

a. A block of solid paraffin (wax) in molasses. 

b. A bar of gold in mercury. 

c. A piece of platinum in gasoline. 

d. A block of paraffin in gasoline. 

material density (g/ cm 3 ) 

gasoline 0.7 

gold 19.3 

lead 11.3 

mercury 13.6 

molasses 1.37 

paraffin 0.87 

platinum 21.4 

10.4

Name: Date: 

11.1 Layers of the Atmosphere 

Use the table below to organize the information in Section 11.1 of your text. You can use the table as a study 

guide as you review for tests. 

Layer Distance from 

Earth’s Surface 

Troposphere 

Stratosphere 

Mesosphere 

Thermosphere 

Exosphere 

Thickness Facts 

11.1

Page 1 of 2 

11.2 Gaspard Gustave de Coriolis 

Gaspard Gustave de Coriolis was a French mechanical engineer and mathematician in the early 

1800’s. His name is famous today for his work on wind deflection by the Coriolis effect. 

From Paris to Nancy to Paris again 

Gaspard Gustave de Coriolis 

(Kor-e-olis) was born in 1792 

in Paris, France. 

Shortly after his birth, his 

family left Paris and settled in 

the town of Nancy, 

pronounced nasi in French. It 

was here in Nancy that 

Coriolis grew up and attended 

school. 

He was exceptionally gifted in 

the area of mathematics, and took the entrance exam for 

Ecole Polytechnique when he was 16 years old. Ecole is 

French for school. Ecole Polytechnique is one of the bestknown 

French Grandes ecoles (Great Schools) for 

engineering. Coriolis ranked second out of all the students 

entering Ecole Polytechnique that year. 

After graduating from Ecole Polytechnique, he continued 

his studies at Ecole des Ponts et Chaussees (School of 

Bridges and Roads) in Paris. 

Then Coriolis’ dreams of becoming an engineer were put 

on hold. Faced with the responsibility of supporting his 

family after his father’s death in 1816, he accepted a 

position as a tutor in mathematical analysis and mechanics 

back at Ecole Polytechnique. At this time, Coriolis was 

only 24 years old. 

The tutor becomes a professor 

Coriolis earned great respect for his studies and research in 

mechanics, engineering, and mathematics. He published his 

first official work in 1829 titled On the Calculation of 

Mechanical Action. This same year he became professor of 

mechanics at Ecole Centrales des Artes et Manufactures. 

Coriolis became one of the leading scientific thinkers by 

introducing the terms work and kinetic energy. 

In 1830 he once again found himself back at Ecole 

Polytechnique after accepting the position of professor. 

Coriolis went on to be elected chair of the Academie des 

Sciences, and later appointed director of studies at Ecole 

Polytechnique. 

11.2 

The paper that made him famous 

In 1835, Coriolis published the paper that made his name 

famous: On the Equations of Relative Motion of Systems of 

Bodies. The paper discussed the transfer of energy in 

rotating systems. Coriolis’s research helped explain how 

the Earth’s rotation causes the motion of air to curve with 

respect to the surface of the Earth. 

His name did not become linked with meteorology until the 

beginning of the twentieth century. He is noted for the 

explanation of the bending of air currents known as the 

Coriolis effect. 

Bending of currents 

There are patterns of winds that naturally cover the Earth. 

The global surface wind patterns in the northern and 

southern hemisphere bend due to the Earth’s rotation. 

For example, the Coriolis effect bends the trade winds 

moving across the surface. They flow from northeast to 

southwest in the northern hemisphere, and from southwest 

to northeast in the southern hemisphere. 

The Coriolis effect has helped scientist explain many 

rotational patterns, yet it does not determine the direction of 

water draining in sinks, bathtubs, and toilets (as some have 

suggested). However, it does explain the rotation of 

cyclones. 

Gaspard Gustave de Coriolis died in 1843 in Paris.

Page 2 of 2 


1. How did Coriolis’s education influence his work? 

2. Explain the importance of Coriolis’s first book titled On the Calculation of Mechanical Action. 

3. To understand why Earth’s rotation affects the path of air currents, imagine the following situation: You are a pilot who 

wants to fly an airplane from St. Paul, Minnesota, 700 miles south to Little Rock, Arkansas. If you set your compass and 

try to fly straight south, you will probably end up in New Mexico! Why would you end up in New Mexico instead of Little 

Rock? 

4. Compare the Coriolis effect in the northern hemisphere with the Coriolis effect in the southern hemisphere. 

5. Research the following global surface wind patterns: trade winds, polar easterlies, prevailing westerlies, and explain 

the Coriolis effect on each wind pattern. 

6. Research why Coriolis’s work on Earth’s rotation was not accepted until long after his death in 1843. 

7. Research the other books that Coriolis wrote, such as Mathematical Theory of the Game of Billiards and Treatise on the 

Mechanics of Solid Bodies, and explain their scientific impact. 

11.2

Name: Date: 

11.2 Degree Days 

Freezing winter weather or sweltering summer heat—in either condition, people use energy to keep their homes, 

schools, and businesses comfortable. You can use degree day values to help predict how much energy will be 

needed each month to heat or cool a building. In this activity, you will learn how degree day values are calculated 

and how to use them to evaluate energy needs. 

Understanding degree days 

Degree day values are calculated by comparing a day’s average 

temperature to 65 °Fahrenheit. The more extreme the temperature, the 

higher the degree day value. For example, if the average daily 

temperature were 72°F, the degree day value would be 72 minus 65, or 

7. On a day with an average temperature of 35°F, the degree day value 

would be 65 minus 35, or 30. 

When the average daily temperature is lower than 65°F, we use the term 

heating degree day value, because you need to add heat to a building 

to bring it to a comfortable temperature. When the average daily 

temperature is higher than 65°F, we talk about the cooling degree day 

value. 

We compare the daily average temperature to 65°F because 65°F is a 

temperature at which most people are comfortable without heating or air 

conditioning. If the average temperature is close to 65°F, you won’t need 

to spend much money heating or cooling your home that day. However, if 

the average temperature is well above or below 65°F, you’ll be spending 

a lot more money on electricity or fuel. 

1. On July 22, 2002, the average daily temperature in St. Louis, Missouri, was 88°F. Calculate the cooling 

degree day value. 

2. On January 22, 2003, the average daily temperature in St. Louis was 14°F. Calculate the cooling degree day 

value. 

3. On which day—July 22, 2002 or January 22, 2003—was the heating degree day value zero? On which day 

was the cooling degree day value zero? 

11.2

Page 2 of 3 

Using temperature data to calculate degree day values 

The table below shows temperature data recorded by the National Weather Service in May 2003. 

Day High temp 

(°F) 

Table 1: Temperature data for St. Louis, May 1-14, 2003 

Low temp 

(°F) 

Average temp 

(high +low)÷2 

Heating 

degree day value 

Cooling 

degree day value 

1 73 61 (73 + 61)¸2 = 67 0 2 

2 63 52 

3 70 44 

4 65 52 

5 83 58 

6 79 59 

7 74 60 

8 71 53 

9 90 70 

10 82 62 

11 65 52 

12 71 52 

13 74 56 

14 75 60 

Two week totals: 

1. Calculate the average temperature, the heating degree day value, and the cooling degree day value for each 

day. Record your answers in the Table 1. The first one is done for you. 

2. During the first two weeks of May, on how many days were St. Louis residents more likely to use their 

heating systems? On how many days were they more likely to cool their homes? 

Calculating monthly totals for degree day values 

3. Find the sum of the numbers in the fifth column of Table 1. This will give you the total heating degree day 

value for May 1–14, 2003. Record your answer in the table’s last row. 

4. Find the total cooling degree day value for same time period by finding the sum of the sixth column of 

Table 1. Record your answer in the table’s last row. 

5. The total heating degree day value for May 15-31, 2003 was 31. The total cooling degree day value was 32. 

Find the monthly total heating and cooling degree day values. 

6. In St. Louis, the average total heating degree day value for May is 79. The average total cooling degree day 

value for May is 114. How was May 2003 different from the average? Do you think residents used more 

energy than usual to keep their homes comfortable, or less? 

11.2

Page 3 of 3 

Using average monthly degree day values 

The National Weather Service provides average monthly degree day values to help citizens better 

evaluate their energy needs. 

Average monthly heating degree day (HDD) and cooling degree day (CDD) values for St. Louis 

1. On a separate piece of paper, make a bar graph showing the average monthly heating and cooling degree day 

values for St. Louis. Place months on the x-axis and monthly average degree day values on the y-axis. Use 

red bars for the heating degree day values and blue bars for the cooling degree day values. Use your graph to 

answer the following questions: 

2. In which month should a St. Louis resident budget the most money for heating costs? 

3. In which month should a St. Louis resident budget the most money for cooling costs? 

4. 

January February March April May June 

HDD CDD HDD CDD HDD CDD HDD CDD HDD CDD HDD CDD 

1097 0 844 0 613 7 294 32 79 114 6 316 

Average monthly heating degree day (HDD) and cooling degree day (CDD) values for St. Louis 

July August September October November December 

HDD CDD HDD CDD HDD CDD HDD CDD HDD CDD HDD CDD 

0 461 1 396 46 196 246 36 583 3 949 0 

a In which month do you think a St. Louis resident will spend the least amount of money to keep their home 

at a comfortable temperature? Explain. 

b Challenge! What additional information would you need to calculate the actual monthly heating and 

cooling costs for a particular building? 

All climate data courtesy of the National Weather Service St. Louis Weather Station. 

11.2

Page 1 of 2 

11.3 Joanne Simpson 

11.3 

Dr. Joanne Simpson was the first woman to serve as president of the American Meteorological Society. 

Her road to success was not easy. She chose to forge ahead in the field of meteorology for the sake of women 

who would enter the field after her. 

Early goals 

Joanne Simpson was born in 

1923 in Boston, 

Massachusetts. At a young 

age, Simpson was 

determined to have a career 

that would provide her with 

financial independence. Her 

mother, a journalist, 

remained in a difficult 

marriage because she could 

not afford to provide for her 

children on her own. 

Simpson knew at age ten that 

she wanted to be able to support herself and any future 

children. 

So Simpson’s journey began. As a child, Simpson loved 

clouds. She spent time gazing at clouds when she sailed 

off the Cape Cod coast. Simpson’s father, aviation editor 

for the Boston Herald newspaper, probably sparked 

Simpson’s interest in flight. Joanne loved to fly and 

earned her pilot’s license at 16. Her interest in weather 

took off. 

The sky’s the limit 

Simpson earned her degree from the University of 

Chicago in 1943. It was here that she developed a love 

for science. She planned to study astrophysics. However, 

as a student pilot she was required to take a meteorology 

course. Meteorology was fascinating. She wanted to take 

more courses. Carl-Gustaf Rossby, a great twentieth 

century meteorologist, had just started an institute of 

meteorology at the university. Simpson met with Rossby 

and enrolled in the World War II meteorology program 

as a teacher-in-training. She taught meteorology to 

aviation cadets. 

Women temporarily filled the roles of men away at war. 

At the end of the war, most women returned home, but 

not Simpson. She completed a master’s degree and 

wanted to earn a Ph.D. Her advisor said that women did 

not earn Ph.D.s in meteorology. The all-male faculty felt 

that women were unable to do the work which included 

night shifts and flying planes. She was even told that if 

she earned the degree no one would ever hire a woman. 

Determined even more, Simpson pursued her dream. She 

took a course with Herbert Riehl, a leader in the field of 

tropical meteorology. She asked Riehl if he would be her 

advisor and he agreed. Not surprisingly, Simpson chose 

to study clouds. Her new advisor thought it would be a 

perfect topic “for a little girl to study.” Throughout her 

Ph.D. program, she studied in an unsupportive academic 

environment. She persevered and became the first 

woman to earn a Ph.D. in meteorology. 

Working woman 

As a woman, Simpson did have difficulty finding a job. 

Eventually she became an assistant physics professor. 

Two years later, she took a job at Woods Hole 

Oceanographic Institute to study tropical clouds. People 

at the time believed clouds were produced by the 

weather and were not the cause for weather. Simpson, 

studying cumulus clouds in the tropics, proved that 

clouds do affect the weather. She found that very tall 

clouds near the equator created enough energy to 

circulate the atmosphere. Together, Simpson and Riehl 

developed the “Hot Tower Theory.” Tall cloud towers 

can carry moist ocean air as high as 50,000 feet into the 

air, create heat, and release energy. 

While studying hurricanes, Simpson discovered that hot 

towers release energy to the hurricane eye and act as the 

hurricane’s engine. Simpson’s work with clouds 

continued as she created the first cloud model. Using a 

slide rule, she created a model well before computers 

were invented. She later became the first person to create 

a computerized cloud model. 

A life of achievement 

Simpson’s career spans many decades, many 

institutions, and many positions. She has won numerous 

awards including the Carl-Gustaf Rossby Research 

Award. In 1979, she joined NASA’s Goddard Space 

Flight Center and enjoyed finally working with other 

female scientists. As a NASA chief scientist, Simpson 

does not plan to retire. Today, she continues to study 

rainfall, satellite images, and hurricanes.

Page 2 of 2 


1. Dr. Simpson achieved many “firsts” in the field of meteorology. Identify three of these first time 

achievements. 

2. Simpson’s road to success in the field of meteorology was not easy. What obstacles did she overcome on her 

journey to eventual success? 

3. What have you learned about working towards goals based on Simpson’s biography? 

4. Research: What is a slide rule? What caused the slide rule to fade from use? 

5. Research: What is the Carl-Gustaf Rossby Research Award? 

6. Research: Where is the Woods Hole Oceanographic Institute located and what does it do? 

7. Research: Use a library or the Internet to find a photo or sketch of hot tower clouds. Present the image to 

your class, citing your source. 

11.3

Name: Date: 

11.3 Weather Maps 

You have learned how the Sun heats Earth and how the heating of land is different than the heating of water. In 

this skill sheet, you will analyze the national weather forecast and make inferences as to what causes differences 

in weather across the nation. To complete this skill sheet, you will need a national weather forecast from a daily 

newspaper and a map of North America from an atlas. 

Analyzing temperature 

Study the national weather forecast from a daily newspaper. Locate the list of the temperature and sky cover in 

cities around the country. Also, locate the weather map showing sunny regions, the temperature, high- and lowpressure 

regions, and fronts. Record the high and low temperatures for cities in the table below. Then find the 

difference between the two temperature readings. Sky cover and pressure will be filled in later. 

City High Low Temp difference Sky cover Pressure 

Seattle, Washington 

Los Angeles, California 

Las Vegas, Nevada 

Phoenix, Arizona 

Atlanta, Georgia 

Tampa, Florida 

San Francisco, California 

Oklahoma City, Oklahoma 

New Orleans, Louisiana 

Kansas City, Kansas 

Tucson, Arizona 

Denver, Colorado 

Dallas, Texas 

Houston, Texas 

Minneapolis, Minnesota 

Memphis, Tennessee 

Chicago, Illinois 

Miami, Florida 

New York, New York 

Baltimore, Maryland 

11.3

Page 2 of 2 

What causes the wide variety of temperature conditions across the map? 

Use the table on the first page to respond to the following questions. It will also be helpful for you to 

study a map of the United States that includes the Pacific and Atlantic Oceans and details about major 

topographical features. 

1. Give examples of differences in the cities’ high temperatures due to latitude. For example, Dallas, Texas is 

in a lower latitude than Seattle, Washington. Explain why these differences exist. 

2. Give examples of differences in the cities’ high temperatures due to geographical features such as the Pacific 

Ocean, the Rocky Mountains, the Great Lakes, or the Atlantic Ocean. Explain why geography influences 

temperatures. 

3. Fill in the table for the sky cover for each city. How does the sky cover affect the temperatures of cities near 

the same latitude? Why do you think this is? 

What does atmospheric pressure tell us about the weather? 

4. On your weather map, over which states are areas of high pressure centered? Over which states are lowpressure 

areas centered? 

5. In the sixth column of the table (the heading is Pressure), record whether you think each city is in a region of 

high pressure, low pressure, or in-between. 

6. What kind of cloud cover or weather is associated with high-pressure regions? Look at the sky cover for the 

cities in the high-pressure regions. What do you think the humidity is like in these regions? 

7. What kind of cloud cover or weather is associated with low-pressure regions? Look at the sky cover for the 

cities in the low-pressure regions. What do you think the humidity is like in these regions? 

8. Locate the fronts shown on the weather map. The flags on the fronts tell us the direction of the wind. The 

cold fronts are symbolized by triangular flags, the warm fronts by semicircular flags. Are fronts associated 

with high- or low-pressure regions? 

9. What type of weather is associated with a warm front? What type of weather is associated with a cold front? 

10. Based on what you have learned so far about low- and high-pressure regions, let’s investigate the effect they 

have on the wind. High-pressure regions tend to push air toward low-pressure regions. Do you think the air 

in a low-pressure region tends to sink or rise? Does the air in a high-pressure region sink or rise? 

11. Based on those conclusions, how do you think low-pressure regions contribute to the formation of 

rainstorms? 

12. Precipitation occurs when warm, moist air is cooled to a certain temperature called the dew point. At the dew 

point temperature water in the air condenses into droplets of water called “dew” and soon these droplets fall 

out of the sky as precipitation. Why would a low-pressure region be a good place for a volume of air to reach 

the dew point temperature? 

11.3

Name: Date: 

11.3 Tracking a Hurricane 

Hurricane Andrew (August 1992) was one of the most devastating storms of the twentieth century. Originally 

labelled a Category 4 storm, it was recently upgraded to a Category 5, the most severe type of hurricane. 

Scientists use satellite data and weather instruments dropped by aircraft to measure the storm’s intensity. As 

research techniques improve, weather experts can more accurately analyze data collected by these instruments. 

NOAA scientists have now determined that Andrew’s sustained winds reached at least 165 miles per hour. In this 

activity, you will track Hurricane Andrew’s treacherous journey. 

The storm’s beginning 

Hurricane Andrew was born as a result of a tropical wave which moved off the west coast of Africa and passed 

south of the Cape Verde Islands. On August 17, 1992, it became a tropical storm. That means it had sustained 

winds of 39-73 miles per hour. 

1. At 1200 Greenwich Mean Time (GMT) on August 17, Tropical Storm Andrew was located at 

12.3°N latitude and 42.0°W longitude. The wind speed was 40 miles per hour. Plot the storm’s location on 

your map. 

2. For the next four days, Tropical Storm Andrew moved uneventfully west-northwest across the Atlantic. Plot 

the storm’s path as it traveled toward the Caribbean Islands. 

Table 1:Tropical Storm Andrew’s path 

Date Time (GMT) Latitude (°N) Longitude (°W) Wind speed (mph) 

8/18/1992 1200 14.6 49.9 52 

8/19/1992 1200 18.0 56.9 52 

8/20/1992 1200 21.7 60.7 46 

8/21/1992 1200 24.4 64.2 58 

11.3

Page 2 of 4 

The storm intensifies 

Late on August 21, a deep high pressure center developed over the southeastern United States and 

extended eastward to an area just north of Tropical Storm Andrew. In response to this more favorable 

environment, the storm strengthened rapidly and turned westward. At 1200 GMT on August 22, the storm 

reached hurricane status, meaning it had sustained winds of at least 74 miles per hour. 

1. Plot Hurricane Andrew’s path over the next two days. 

Table 2:Hurricane Andrew’s path 


8/22/1992 1200 25.8 68.3 81 

8/23/1992 1200 25.4 74.2 138 

2. Hurricane watches are issued when hurricane conditions are possible in the area, usually within 36 hours. 

Hurricane warnings are issued when hurricane conditions are expected in the area within 24 hours. Look at 

the distance the hurricane travelled in the last 24 hours and use that information to predict where it might be 

in 24 hours, and in 36 hours. Name one area that you would declare under a hurricane watch, and an area that 

you would declare under a hurricane warning. 

Landfall 

On the evening of August 23, Hurricane Andrew first made landfall. Landfall is defined as when the center of the 

hurricane’s eye is over land. 

1. Plot the point of Hurricane Andrew’s first landfall. 

Table 3:Hurricane Andrew’s first landfall 


8/23/1992 2100 25.4 76.6 150 

2. Where did this first landfall occur? 

11.3

Page 3 of 4 

Hurricane Andrew crosses the Gulf Stream and strikes the U.S. 

11.3 

During the night of August 23, Hurricane Andrew briefly weakened as it moved over land. However, 

once the storm moved back over open waters, it rapidly regained strength. The warm water of the Gulf Stream 

increased the intensity of the hurricane’s convection cycle. At 0905 GMT on August 24, Hurricane Andrew 

made landfall again. 

1. Plot the point of Hurricane Andrew’s next landfall. 

2. Where did this landfall occur? 

The final landfall 

Table 4:Hurricane Andrew’s next landfall 


8/24/1992 0905 25.5 80.3 144 

After making its first landfall in the United States (where it caused an estimated $25 billion in damage), 

Hurricane Andrew moved northwest across the Gulf of Mexico. On the morning of August 26, 1992, Hurricane 

Andrew made its final landfall. Afterward, Andrew weakened rapidly to tropical storm strength in about 10 

hours, and then began to dissipate. 

1. Plot Andrew’s course across the Gulf of Mexico and its final landfall. 

Table 5:Hurricane Andrew’s next landfall 


8/24/1992 1800 25.8 83.1 133 

8/25/1992 1800 27.8 89.6 138 

8/26/1992 0830 29.6 91.5 121 

2. In which state did Hurricane Andrew’s final landfall occur? 

Hurricane information provided by National Oceanographic and Atmospheric Administration’s National 

Hurricane Center.

Page 4 of 4 

11.3

Name: Date: 

12.1 Structure of the Atom 

Atoms are made of three tiny subatomic particles: protons, neutrons, and 

electrons. The protons and neutrons are grouped together in the nucleus, 

which is at the center of the atom. The chart below compares electrons, 

protons, and neutrons in terms of charge and mass. 

The atomic number of an element is the number of protons in the nucleus 

of every atom of that element. 

Isotopes are atoms of the same element that have different numbers of 

neutrons. The number of protons in isotopes of an element is the same. 

The mass number of an isotope tells you the number of protons plus the number of neutrons. 

Mass number = number of protons + number of neutrons 

• Carbon has three isotopes: carbon-12, carbon-13, and carbon-14. The atomic number of carbon is 6. 

a. How many protons are in the nucleus of a carbon atom? 

Solution: 

6 protons 

The atomic number indicates how many protons are in the nucleus of an atom. All atoms of carbon have 

6 protons, no matter which isotope they are. 

b. How many neutrons are in the nucleus of a carbon-12 atom? 

Solution: 

the mass number - the atomic number = the number of neutrons. 

12 – 6 = 6 

6 neutrons 

c. How many electrons are in a neutral atom of carbon-13? 

Solution: 

6 electrons. All neutral carbon atoms have 6 protons and 6 electrons. 

d. How many neutrons are in the nucleus of a carbon-14 atom? 

Solution: 

the mass number - the atomic number = the number of neutrons 

14 – 6 = 8 

8 neutrons 

12.1

Page 2 of 2 

Use a periodic table of the elements to answer these questions. 

1. The following graphics represent the nuclei of atoms. Using a periodic table of elements, fill in the table. 

What the 

nucleus looks 

like 

What is this 

element? 

How many electrons does 

the neutral atom have? 

2. How many protons and neutrons are in the nucleus of each isotope? 

a. hydrogen-2 (atomic number = 1) 

b. scandium-45 (atomic number = 21) 

c. aluminum-27 (atomic number = 13) 

d. uranium-235 (atomic number = 92) 

e. carbon-12 (atomic number = 6) 

What is the mass 

number? 

3. Although electrons have mass, they are not considered in determining the mass number of an atom. Why? 

4. A hydrogen atom has one proton, two neutrons, and no electrons. Is this atom an ion? Explain your answer. 

5. An atom of sodium-23 (atomic number = 11) has a positive charge of +1. Given this information, how many 

electrons does it have? How many protons and neutrons does this atom have? 

12.1

Name: Date: 

12.1 Atoms and Isotopes 

You have learned that atoms contain three smaller particles called protons, neutrons, and electrons, and that the 

number of protons determines the type of atom. How can you figure out how many neutrons an atom contains, 

and whether it is neutral or has a charge? Once you know how many protons and neutrons are in an atom, you can 

also figure out its mass. 

In this skill sheet, you will learn about isotopes, which are atoms that have the same number of protons but 

different numbers of neutrons. 

What are isotopes? 

In addition to its atomic number, every atom can also be described by its mass number: 

mass number = number of protons + number of neutrons 

Atoms of the same element always have the same number of protons, but can have different numbers of neutrons. 

These different forms of the same element are called isotopes. 

Sometimes the mass number for an element is included in its symbol. When the 

symbol is written in this way, we call it isotope notation. The isotope notation for 

carbon-12 is shown to the right. How many neutrons does an atom of carbon-12 

have? To find out, simply take the mass number and subtract the atomic number: 

12 – 6 = 6 neutrons. 

Hydrogen has three isotopes as shown below. 

1. How many neutrons does protium have? What about deuterium and tritium? 

2. Use the diagram of an atom to answer the questions: 

a. What is the atomic number of the element? 

b. What is the name of the element? 

c. What is the mass number of the element? 

d. Write the isotope notation for this isotope. 

12.1

Page 2 of 2 

What is the atomic mass? 

If you look at a periodic table, you will notice that the atomic number increases by one whole number at a time. 

This is because you add one proton at a time for each element. The atomic mass however, increases by amounts 

greater than one. This difference is due to the neutrons in the nucleus. The value of the atomic mass reflects the 

abundance of the stable isotopes for an element that exist in the universe. 

Since silver has an atomic mass of 107.87, this means that most of the stable isotopes that exist have a mass 

number of 108. In other words, the most common silver isotope is “silver-108.” To figure out the most common 

isotope for an element, round the atomic mass to the nearest whole number. 

1. Look up bromine on the periodic table. What is the most common isotope of bromine? 

2. Look up potassium. How many neutrons does the most common isotope of potassium have? 

3. Look up lithium. What is its most common isotope? 

4. How many neutrons does the most common isotope of neon have? 

12.1

Name: Date: 

12.1 Ernest Rutherford 

12.1 

Ernest Rutherford initiated a new and radical view of the atom. He explained the mysterious 

phenomenon of radiation as the spontaneous disintegration of atoms. He was the first to describe the atom’s 

internal structure and performed the first successful nuclear reaction. 

Ambitious immigrants 

Ernest Rutherford was born 

in rural New Zealand on 

August 31, 1871. His father 

was a Scottish immigrant, his 

mother English. Both valued 

education and instilled a 

strong work ethic in their 12 

children. Ernest enjoyed the 

family farm, but was 

encouraged by his parents 

and teachers to pursue 

scholarships. He first received a scholarship to a 

secondary school, Nelson College. Then, in 1890, 

after twice taking the qualifying exam, he received a 

scholarship to Canterbury College of the University of 

New Zealand. 

Investigating radioactivity 

After earning three degrees in his homeland, 

Rutherford traveled to Cambridge, England, to pursue 

graduate research under the guidance of the man who 

discovered the electron, J. J. Thomson. Through his 

research with Thomson, Rutherford became interested 

in studying radioactivity. In 1898 he described two 

kinds of particles emitted from radioactive atoms, 

calling them alpha and beta particles. He also coined 

the term half-life to describe the amount of time taken 

for radioactivity to decrease to half its original level. 

An observer of transformations 

Rutherford accepted a professorship at McGill 

University in Montreal, Canada, in 1898. It was there 

that he proved that atoms of a radioactive element 

could spontaneously decay into another element by 

expelling a piece of the atom. This was surprising to 

the scientific community—the idea that atoms could 

change into other atoms had been scorned as alchemy. 

In 1908 Rutherford received the Nobel Prize in 

chemistry for “his investigations into the 

disintegration of the elements and the chemistry of 

radioactive substances.” He considered himself a 

physicist and joked that, “of all the transformations I 

have seen in my lifetime, the fastest was my own 

transformation from physicist to chemist.” 

Exploring atomic space 

Rutherford had returned to England in 1907, to 

Manchester University. There, he and two students 

bombarded gold foil with alpha particles. Most of the 

particles passed through the foil, but a few bounced 

back. They reasoned these particles must have hit 

denser areas of foil. 

Rutherford hypothesized that the atom must be mostly 

empty space, through which the alpha particles 

passed, with a tiny dense core he called the nucleus, 

which some of the particles hit and bounced off. From 

this experiment he developed a new “planetary 

model” of the atom. The inside of the atom, 

Rutherford suggested, contained electrons orbiting a 

small nucleus the way the planets of our solar system 

orbit the sun. 

‘Playing with marbles’ 

In 1917, Rutherford made another discovery. He 

bombarded nitrogen gas with alpha particles and 

found that occasionally an oxygen atom was 

produced. He concluded that the alpha particles must 

have knocked a positively charged particle (which he 

named the proton) from the nucleus. He called this 

“playing with marbles” but word quickly spread that 

he had become the first person to split an atom. 

Rutherford, who was knighted in 1914 (and later 

elevated to the peerage, in 1931) returned to 

Cambridge in 1919 to head the Cavendish Laboratory 

where he had begun his research in radioactivity. He 

remained there until his death at 66 in 1937.

Page 2 of 2 


1. What are alpha and beta particles? Use your textbook to find the definitions of these terms. Make a 

diagram of each particle; include labels in your diagram. 

2. The term “alchemy” refers to early pseudoscientific attempts to transform common elements into more 

valuable elements (such as lead into gold). For one kind of atom to become another kind of atom, which 

particles of the atom need to be expelled or gained? 

3. Make a diagram of the “planetary model” of the atom. Include the nucleus and electrons in your diagram. 

4. Compare and contrast Rutherford’s “planetary model” of the atom with our current understanding of an 

atom’s internal structure. 

5. Why did Rutherford say that bombarding atoms with particles was like “playing with marbles”? What 

subatomic particle did Rutherford discover during this phase of his work? 

6. Choose one of Rutherford’s discoveries and explain why it intrigues you. 

12.1

Name: Date: 

12.2 Electrons and Energy Levels 

Danish physicist Neils Bohr (1885–1962) proposed the concept of energy levels to explain electron behavior in 

atoms. While we know today that his model doesn’t explain everything about how electrons behave, it is still a 

useful starting point for understanding what is happening inside atoms. 

The number of electrons in an atom is equal to the number of protons in the nucleus. That means each element 

has a different number of electrons and therefore fills the energy levels to a different point. The innermost energy 

level is filled first, and then each additional electron occupies the lowest unfilled energy level in the atom. 

An atom of the element carbon has six electrons. Show how the electrons are arranged in energy levels. 

Solution 

Note: remember that atoms are actually three-dimensional, and that it is 

impossible to show the exact location of a particular electron within the 

electron cloud. Therefore, as long as the entire first energy level is filled, 

and four of the spaces in the second level are filled, the answer is 

acceptable. However, because electrons repel each other, it is standard 

procedure to show the electrons evenly spaced within the energy level. 

Answer the following questions about electrons and energy levels. Use section 12.2 of your text if needed. 

1. Who proposed the concept of energy levels inside atoms? 

2. Explain how energy levels are like a set of stairs. Where can electrons exist? 

3. In a stable atom, how are the energy levels filled? 

4. Show how the electrons of the following atoms are arranged in energy levels. 

a. Chlorine-17 electrons b. Oxygen-8 electrons c. Aluminum- 13 electrons d. Argon- 18 electrons 

e. Copper- 29 electrons f. Calcium-20 electrons 

12.2

Name: Date: 

12.2 Niels Bohr 

12.2 

Danish physicist Niels Bohr first proposed the idea that electrons exist in specific orbits around the 

atom’s nucleus. He showed that when an electron falls from a higher orbital to a lower one, it releases energy in 

the form of visible light. 

At home among ideas 

Niels Bohr was born October 

7, 1885, in Copenhagen, 

Denmark. His father was a 

physiology professor at the 

University of Copenhagen, 

his mother the daughter of a 

prominent Jewish politician 

and businessman. His parents 

often invited professors to the 

house for dinners and 

discussions. 

Niels and his sister and brother were invited to join 

this friendly exchange of ideas. (Niels and his brother 

also shared a passion for soccer, which they both 

played, and for which Harald, later a world-famous 

mathematician, was to win an Olympic silver medal.) 

Bohr entered the University of Copenhagen in 1903 to 

study physics. Because the university had no physics 

laboratory, Bohr conducted experiments in his father’s 

physiology lab. He graduated with a doctorate in 1911. 

Meeting of great minds 

In 1912, Bohr went to Manchester, England, to study 

under Ernest Rutherford, who became a lifelong 

friend. Rutherford had recently published his new 

planetary model of the atom, which explained that an 

atom contains a tiny dense core surrounded by 

orbiting electrons. 

Bohr began researching the orbiting electrons, hoping 

to describe their behavior in greater detail. 

Electrons and the atom’s chemistry 

Bohr studied the quantum ideas of Max Planck and 

Albert Einstein as he attempted to describe the 

electrons’ orbits. In 1913 he published his results. He 

proposed that electrons traveled only in specific orbits. 

The orbits were like rungs on a ladder— electrons 

could move up and down orbits, but did not exist in 

between the orbital paths. 

He explained that outer orbits could hold more 

electrons than inner orbits, and that many chemical 

properties of the atom were determined by the number 

of electrons in the outer orbit. 

Bohr also described how atoms emit light. He 

explained that an electron needs to absorb energy to 

jump from an inner orbit to an outer one. When the 

electron falls back to the inner orbit, it releases that 

energy in the form of visible light. 

An institute, then a Nobel Prize 

In 1916, Bohr accepted a position as professor of 

physics at the University of Copenhagen. The 

University created the Institute of Theoretical Physics 

that Bohr directed for the rest of his life. In 1922, he 

was awarded the Nobel Prize in physics for his work 

in atomic structure and radiation. 

In 1940, World War II spread across Europe and 

Germany occupied Denmark. Though he had been 

baptized a Christian, Bohr’s family history and his 

own anti-Nazi sentiments made life difficult. 

In 1943, he escaped in a fishing boat to Sweden, 

where he convinced the king to offer sanctuary to all 

Jewish refugees from Denmark. The British offered 

him a position in England to work with researchers on 

the atomic bomb. A few months later, the team went to 

Los Alamos, New Mexico, to continue their work. 

A warrior for peace 

Although Bohr believed the creation of the atomic 

bomb was necessary in the face of the Nazi threat, he 

was deeply concerned about its future implications. 

Bohr promoted disarmament efforts through the 

United Nations and won the first U.S. Atoms for 

Peace Award in 1957, the same year his son Aage. 

shared the Nobel Prize in physics. He died in 1962 in 

Copenhagen.

Page 2 of 2 


1. How did Niels Bohr’s model of the atom compare with Ernest Rutherford’s? 

2. Name two specific contributions Bohr made to our understanding of atomic structure. 

3. Make a drawing of Bohr’s model of the atom. 

4. In your own words describe how atoms emit light. 

5. Why do you think Bohr was concerned with the future implications of his work on atomic bombs? 

12.2

Name: Date: 

12.3 The Periodic Table 

Many science laboratories have a copy of the periodic table of the elements on display. This important 

chart holds an amazing amount of information. In this skill sheet, you will use a periodic table to identify 

information about specific elements, make calculations, and make predictions. 

Periodic table primer 

To work through this skill sheet, you will use the periodic table of the 

elements. The periodic table shows five basic pieces of information. 

Four are labeled on the graphic at right; the fifth piece of information is 

the location of the element in the table itself. The location shows the 

element group, chemical behavior, approximate atomic mass and size, 

and other characteristic properties. 

Review: Atomic number, Symbol, and Atomic Mass 

Use the periodic table to find the answers to the following questions. As you become more familiar with the 

layout of the periodic table, you’ll be able to find this information quickly. 

Atomic Number: Write the name of the element that corresponds to each of the following atomic numbers. 

1. 9 2. 18 3. 25 4. 15 5. 43 

6. What does the atomic number tell you about an element? 

Symbol and atomic mass: For each of the following, write the element name that corresponds to the symbol. In 

addition, write the atomic mass for each element. 

7. Fe 8. Cs 9. Si 10. Na 11. Bi 

12. What does the atomic mass tell you about an element? 

13. Why isn’t the atomic mass always a whole number? 

14. Why don’t we include the mass of an atom’s electrons in the atomic mass? 

12.3

Page 2 of 2 

Periodic Table Groups 

The periodic table’s vertical columns are called groups. Groups of elements have similar properties. Use the 

periodic table and the information found in Chapter 15 of your text to answer the following questions: 

15. The first group of the periodic table is known by what name? 

16. Name two characteristics of the elements in the first group. 

17. Name three members of the halogen group. 

18. Describe two characteristics of halogens. 

19. Where are the noble gases found on the periodic table? 

20. Why are the noble gases sometimes called the inert gases? 

Periodic Table Rows 

The rows of the periodic table correspond to the energy levels in the atom. The 

first energy level can accept up to two electrons. The second and third energy 

levels can accept up to eight electrons each. The example to the right shows how 

the electrons of an oxygen atom fill the energy level. 

Show how the electrons are arranged in energy levels in the following atoms:. 

21. He 22. N 23. Ne 24. Al 25. Ar 

Identify each of the following elements:. 

26. 27. 28. 29. 30. 

12.3

Name: Date: 

13.1 Dot Diagrams 

You have learned that atoms are composed of protons, neutrons, and electrons. The electrons occupy energy 

levels that surround the nucleus in the form of an “electron cloud.” The electrons that are involved in forming 

chemical bonds are called valence electrons. Atoms can have up to eight valence electrons. These electrons exist 

in the outermost region of the electron cloud, often called the “valence shell.” 

The most stable atoms have eight valence electrons. When an atom has eight valence electrons, it is said to have 

a complete octet. Atoms will gain or lose electrons in order to complete their octet. In the process of gaining or 

losing electrons, atoms will form chemical bonds with other atoms. One method we use to show an atom’s 

valence state is called a dot diagram, and you will be able to practice drawing these in the following exercise. 

What is a dot diagram? 

Dot diagrams are composed of two parts—the chemical symbol for the element and the dots surrounding the 

chemical symbol. Each dot represents one valence electron. 

• If an element, such as oxygen (O), has six valence electrons, then six dots will surround the 

chemical symbol as shown to the right. 

• Boron (B) has three valence electrons, so three dots surround the chemical symbol for boron as 

shown to the right. 

There can be up to eight dots around a symbol, depending on the number of valence electrons the atom 

has. The first four dots are single, and then as more dots are added, they fill in as pairs. 

Using a periodic table, complete the following chart. With this information, draw a dot diagram for each element 

in the chart. Remember, only the valence electrons are represented in the diagram, not the total number of 

electrons. 

Element Chemical 

symbol 

Potassium K 

Nitrogen N 

Carbon C 

Beryllium Be 

Neon Ne 

Sulfur S 

Total number of 

electrons 

Number of valence 

electrons 

Dot diagram 

13.1

Page 2 of 2 

Using dot diagrams to represent chemical reactivity 

Once you have a dot diagram for an element, you can predict how an atom will achieve a full valence shell. For 

instance, it is easy to see that chlorine has one empty space in its valence shell. It is likely that chlorine will try to 

gain one electron to fill this empty space rather than lose the remaining seven. However, potassium has a single 

dot or electron in its dot diagram. This diagram shows how much easier it is to lose this lone electron than to find 

seven to fill the seven empty spaces. When the potassium loses its electron, it becomes positively charged. When 

chlorine gains the electron, it becomes negatively charged. Opposite charges attract, and this attraction draws the 

atoms together to form what is termed an ionic bond, a bond between two charged atoms or ions. 

Because chlorine needs one electron, and potassium needs to lose one electron, these two elements can achieve a 

complete set of eight valence electrons by forming a chemical bond. We can use dot diagrams to represent the 

chemical bond between chlorine and potassium as shown above. 

For magnesium and chlorine, however, the situation is a bit different. By examining the electron or Lewis dot 

diagrams for these atoms, we see why magnesium requires two atoms of chlorine to produce the compound, 

magnesium chloride, when these two elements chemically combine. 

Magnesium can easily donate one of its valence electrons to the chlorine to fill chlorine’s valence shell, but this 

still leaves magnesium unstable; it still has one lone electron in its valence shell. However, if it donates that 

electron to another chlorine atom, the second chlorine atom has a full shell, and now so does the magnesium. 

The chemical formula for potassium chloride is KCl. This means that one unit of the compound is made of one 

potassium atom and one chlorine atom. 

The formula for magnesium chloride is MgCl2. This means that one unit of the compound is made of one 

magnesium atom and two chlorine atoms. 

Now try using dot diagrams to predict chemical formulas. Fill in the table below: 

Elements Dot diagram 

for each element 

Na and F 

Br and Br 

Mg and O 

Dot diagram 

for compound formed 

Chemical 

formula 

13.1

Name: Date: 

13.2 Finding the Least Common Multiple 

Knowing how to find the least common multiple of two or more numbers is helpful in physical science classes. 

You need to find the least common multiple in order to add fractions with different denominators, or to predict 

the chemical formula of many common compounds. 

The least common multiple is the smallest multiple of two or more whole numbers. To find the least common 

multiple of 3 and 4, simply list the multiples of each number: 

multiples of 3: 3, 6, 9, 12, 15... 

multiples of 4: 4, 8, 12, 16, 20... 

Then, look for the smallest multiple that occurs in both lists. In this case, the least common multiple is 12. 

Sometimes it’s a little trickier to find the least common multiple. Suppose you are asked to find the least common 

multiple of 15 and 36. Rather than making a long list of multiples, you can use the prime factorization method. 

First, factor each number into primes (remember that prime numbers are numbers that can’t be divided evenly by 

any whole number except one). 

Prime factorization of 15: 3 × 5 

Prime factorization of 36: 3 × 3 × 2 × 2 

Next, create a Venn diagram. Show the factors unique to each number in the separate parts of the circles and the 

factors common to both in the overlapping circles. Since 15 and 36 each have one 3, put one 3 in the middle. 

Finally, multiply all the factors in your diagram from left to right: 

5 × 3 × 3 × 2 × 2 = 180. The least common multiple of 15 and 36 is 180. 

13.2

Page 2 of 2 

13.2 

Important note: If the two numbers each have more than one copy of a certain prime factor, place the 

factor in the overlapping circles as many times as necessary. To find the least common multiple of 60 and 72: 

Prime factorization of 60: 2 × 2 × 3 × 5 

Prime factorization of 72: 2 × 2 × 3 × 2 × 3 

Notice that 2 appears twice in the overlapping circles because 60 and 72 have two 2’s apiece. 

5 × 3 × 2 × 2 × 2 × 3 = 360. The least common multiple of 60 and 72 is 360. 

Find the least common multiple of each of the following pairs of numbers: 

1. 3 and 7 

2. 6 and 8 

3. 9 and 15 

4. 10 and 25 

5. 16 and 40 

6. 21 and 49 

7. 36 and 54 

8. 45 and 63 

9. 55 and 80 

10. 64 and 96

Name: Date: 

13.2 Chemical Formulas 

Compounds have unique names that we use to identify them when we study chemical properties and changes. 

Chemists have devised a shorthand way of representing chemical names that provides important information 

about the substance. This shorthand representation for a compound’s name is called a chemical formula. You will 

practice writing chemical formulas in the following activity. 

What is a chemical formula? 

Chemical formulas have two important parts: chemical symbols for the elements in the compound and subscripts 

that tell how many atoms of each element are needed to form the compound. The chemical formula for water, 

H 2O, tells us that a water molecule is made of the elements hydrogen (H) and oxygen (O) and that it takes two 

atoms of hydrogen and one atom of oxygen to build the molecule. For sodium nitrate, NaNO 3, the chemical 

formula tells us there are three elements in the compound: sodium (Na), nitrogen (N), and oxygen (O). To make a 

molecule of this compound, you need one atom of sodium, one atom of nitrogen, and three atoms of oxygen. 

How to write chemical formulas 

How do chemists know how many atoms of each element are needed to build a molecule? For ionic compounds, 

oxidation numbers are the key. An element’s oxidation number is the number of electrons it will gain or lose in a 

chemical reaction. We can use the periodic table to find the oxidation number for an element. When we add up 

the oxidation numbers of the elements in an ionic compound, the sum must be zero. Therefore, we need to find a 

balance of negative and positive ions in the compound for the molecule to form. 

Example 1: 

A compound is formed by the reaction between magnesium and chlorine. What is the chemical formula for this 

compound? 

From the periodic table, we find that the oxidation number of magnesium is 2+. Magnesium loses 2 electrons in 

chemical reactions. The oxidation number for chlorine is 1-. Chlorine tends to gain one electron in a chemical 

reaction. 

Remember that the sum of the oxidation numbers of the elements in a molecule will equal zero. This compound 

requires one atom of magnesium with an oxidation number of 2+ to combine with two atoms of chlorine, each 

with an oxidation number of 1–, for the sum of the oxidation numbers to be zero. 

(2 + ) + 2(1 − ) = 

0 

To write the chemical formula for this compound, first write the chemical symbol for the positive ion (Mg) and 

then the chemical symbol for the negative ion (Cl). Next, use subscripts to show how many atoms of each 

element are required to form the molecule. When one atom of an element is required, no subscript is used. 

Therefore, the correct chemical formula for magnesium chloride is MgCl 2. 

13.2

Page 2 of 2 

Example 2: 

Aluminum and bromine combine to form a compound. What is the chemical formula for the compound they 

form? 

From the periodic table, we find that the oxidation number for aluminum (Al) is 3+. The oxidation number for 

bromine (Br) is 1–. In order for the oxidation numbers of this compound to add up to zero, one atom of aluminum 

must combine with three atoms of bromine: 

The correct chemical formula for this compound, aluminum bromide, is AlBr 3. 

Practice writing chemical formulas for ionic compounds 

Use the periodic table to find the oxidation numbers of each element. Then write the correct chemical formula for 

the compound formed by the following elements: 

Element Oxidation 

Number 

Potassium (K) Chlorine (Cl) 

Calcium (Ca) Chlorine (Cl) 

Sodium (Na) Oxygen (O) 

Boron (B) Phosphorus (P) 

Lithium (Li) Sulfur (S) 

Aluminum (Al) Oxygen (O) 

Beryllium (Be) Iodine (I) 

Calcium (Ca) Nitrogen (N) 

Sodium (Na) Bromine (Br) 

(3 + ) + 3(1 − ) = 

0 

Element Oxidation 

Number 

Chemical Formula for 

Compound 

13.2

Name: Date: 

13.2 Naming Compounds 

Compounds have unique names that identify them for us when we study chemical properties and changes. 

Predicting the name of a compound is fairly easy provided certain rules are kept in mind. In this skill sheet, you 

will practice naming a variety of chemical compounds. 

Chemical Formulas and Compound Names 

Chemical formulas tell a great deal of information about a compound—the types of elements forming the 

compound, the numbers of atoms of each element in one molecule, and even some indication, perhaps, of the 

arrangement of the atoms when they form the molecule. 

In addition to having a unique chemical formula, each compound has a unique name. These names provide 

scientists with valuable information. Just like chemical formulas, chemical names tell which elements form the 

compound. However, the names may also identify a “family” or group to which the compound belongs. It is 

useful for scientists, therefore, to recognize and understand both a compound’s formula and its name. 

Naming Ionic Compounds 

Naming ionic compounds is relatively simple, especially if the compound is formed only from monoatomic ions. 

Follow these steps: 

1. Write the name of the first element or the positive ion of the compound. 

2. Write the root of the second element or negative ion of the compound. 

3. For example, write fluor- to represent fluorine, chlor- to represent chlorine. 

4. Replace the ending of the negative ion's name with the suffix -ide. 

5. Fluorine → Fluoride; Chlorine → Chloride 

A compound containing potassium (K 1+ ) and iodine (I 1– ) would be named potassium iodide. 

Lithium (Li 1+ ) combined with sulfur (S 2– ) would be named lithium sulfide. 

Naming Compounds with Polyatomic Ions 

Naming compounds that contain polyatomic ions is even easier. Just follow these two steps: 

1. Write the name of the positive ion first. Use the periodic table or an ion chart to find the name. 

2. Write the name of the negative ion second. Again, use the periodic table or an ion chart to find the name. 

A compound containing aluminum (Al 1+ ) and sulfate (SO 4 2– ) would be called aluminum sulfate. 

A compound containing magnesium (Mg 2+ ) and carbonate (CO 3 2– ) would be called magnesium carbonate. 

13.2

Page 2 of 2 

13.2 

Predict the name of the compound formed from the reaction between the following elements and/or 

polyatomic ions. Use the periodic table and the polyatomic ion chart in section 13.2 of your student text to help 

you name the ions. 

Combination Compound Name 

Al + Br 

Be + O 

K+N 

Ba + CrO 4 2– 

Cs + F 

NH 3 1+ +S 

Mg + Cl 

B+I 

Na + SO 4 2– 

Si + C 2H 3O 2 1–

Name: Date: 

13.2 Families of Compounds 

Certain compounds have common characteristics, so we place them into groups or families. The group called 

“enzymes” contains thousands of representative chemicals, but all share certain critical features that allow them 

to be placed into this group. 

The name of a compound often identifies the family of chemical to which it belongs. The clue is usually found in 

the suffix for the compound's name. The table below lists suffixes for some common chemical families. 

Chemical Family Suffix 

Sugars -ose 

Alcohols -ol 

Enzymes -ase 

Ketones -one 

Organic acids -oic or -ic acid 

Alkanes -ane 

Glucose, the compound used by your brain as its primary fuel, is a sugar. The suffix -ose indicates its 

membership in the sugar family. Propane, the compound used to operate your gas barbecue grill, is an alkane, a 

compound formed from carbon and hydrogen atoms that are covalently bonded with single pairs of electrons. We 

know this from the suffix -ane. 

Knowing such information about a compound can be very useful when you are reading the labels of consumer 

products. Compound names can be found in the ingredients list on the label. If you are purchasing a hand lotion 

to alleviate dry skin, you should avoid one that lists a compound with an -ol suffix early in the ingredients list. 

The ingredients are listed from largest amount to smallest amount. The earlier a compound is listed, the greater 

the amount of that compound in the product. A compound with an -ol suffix is an alcohol. Hand lotions with high 

percentages of alcohols are less effective since alcohols tend to dry out rather than moisturize the skin! 

In later chemistry courses, you will learn more about the names and characteristics of “families” of compounds. 

This knowledge will provide you with a powerful tool for making informed consumer decisions. 

13.2

Page 2 of 2 

Using the information in the table on the previous page to predict the chemical family to which the 

following compounds are members: 

Compound Name Chemical Family 

Lipase 

Methanol 

Formic Acid 

Butane 

Sucrose 

Acetone 

Acetic Acid 

13.2

Name: Date: 

14.1 Chemical Equations 

Chemical symbols provide us with a shorthand method of writing the name of an element. Chemical formulas do 

the same for compounds. But what about chemical reactions? To write out, in words, the process of a chemical 

change would be long and tedious. Is there a shorthand method of writing a chemical reaction so that all the 

information is presented correctly and is understood by all scientists? Yes! This is the function of chemical 

equations. You will practice writing and balancing chemical equations in this skill sheet. 

What are chemical equations? 

Chemical equations show what is happening in a chemical reaction. They provide you with the identities of the 

reactants (substances entering the reaction) and the products (substances formed by the reaction). They also tell 

you how much of each substance is involved in the reaction. Chemical equations use symbols for elements and 

formulas for compounds. The reactants are written to the left of the arrow. Products go on the right side of the 

arrow. 

The arrow should be read as “yields” or “produces.” This equation, therefore, says that hydrogen gas (H 2) plus 

oxygen gas (O 2) yields or produces the compound water (H 2O). 

Write chemical equations for the following reactions: 

Reactants Products Unbalanced 

Hydrochloric acid 

HCl 

and 

Sodium hydroxide 

NaOH 

Calcium carbonate 

CaCO 3 

and 

Potassium iodide 

KI 

Aluminum fluoride 

AlF 3 

and 

Magnesium nitrate 

Mg(NO 3 ) 2 

Water 

H 2 O 

and 

Sodium chloride 

NaCl 

H2 + O2 → 

H2O Potassium carbonate 

K 2 CO 3 

and 

Calcium iodide 

CaI 2 

Aluminum nitrate 

Al(NO 3 ) 3 

and 

Magnesium fluoride 

MgF 2 

Chemical Equation 

14.1

Page 2 of 3 

Conservation of atoms 

Take another look at the chemical equation for making water: 

Did you notice that something has been added? 

The large number in front of H 2 tells how many molecules of H 2 are required for the reaction to proceed. The 

large number in front of H 2O tells how many molecules of water are formed by the reaction. These numbers are 

called coefficients. Using coefficients, we can balance chemical equations so that the equation demonstrates 

conservation of atoms. The law of conservation of atoms says that no atoms are lost or gained in a chemical 

reaction. The same types and numbers of atoms must be found in the reactants and the products of a chemical 

reaction. 

Coefficients are placed before the chemical symbol for single elements and before the chemical formula of 

compounds to show how many atoms or molecules of each substance are participating in the chemical reaction. 

When counting atoms to balance an equation, remember that the coefficient applies to all atoms within the 

chemical formula for a compound. For example, 5CH 4 means that 5 atoms of carbon and 20 atoms (5 × 4) of 

hydrogen are contributed to the chemical reaction by the compound methane. 

Balancing chemical equations 

2H2 + O2 → 2H2O To write a chemical equation correctly, first write the equation using the correct chemical symbols or formulas 

for the reactants and products. 

The displacement reaction between sodium chloride and iodine to form sodium iodide and chlorine gas is written 

as: 

NaCl + I2 → 

NaI + Cl2 Next, count the number of atoms of each element present on the reactant and product side of the chemical 

equation: 

Reactant Side of Equation Element Product Side of Equation 

1 Na 1 

1 Cl 2 

2 I 1 

For the chemical equation to be balanced, the numbers of atoms of each element must be the same on either side 

of the reaction. This is clearly not the case with the equation above. We need coefficients to balance the equation. 

14.1

Page 3 of 3 

First, choose one element to balance. Let’s start by balancing chlorine. Since there are two atoms of 

chlorine on the product side and only one on the reactant side, we need to place a “2” in front of the 

substance containing the chlorine, the NaCl. 

This now gives us two atoms of chlorine on both the reactant and product sides of the equation. However, it also 

give us two atoms of sodium on the reactant side! This is fine—often balancing one element will temporarily 

unbalance another. By the end of the process, however, all elements will be balanced. 

We now have the choice of balancing either the iodine or the sodium. Let's balance the iodine. (It doesn’t matter 

which element we choose.) 

There are two atoms of iodine on the reactant side of the equation and only one on the product side. Placing a 

coefficient of “2” in front of the substance containing iodine on the product side: 

There are now two atoms of iodine on either side of the equation, and at the same time we balanced the number 

of sodium atoms! 

In this chemical reaction, two molecules of sodium chloride react with one molecule of iodine to produce two 

molecules of sodium iodide and one molecule of chlorine. Our equation is balanced. 

Balance the following equations using the appropriate coefficients. Remember that balancing one element may 

temporarily unbalance another. You will have to correct the imbalance in the final equation. Check your work by 

counting the total number of atoms of each element—the numbers should be equal on the reactant and product 

sides of the equation. Remember, the equations cannot be balanced by changing subscript numbers! 

1. Al + O2 → Al2O3 2. CO + H2 → H2O + CH4 3. HgO → Hg + O2 4. CaCO3 → CaO + CO2 5. C + Fe2O3 → Fe + CO2 6. N2 + H2 → NH3 7. K + H2O → KOH + H2 8. P + O2 → P2O5 9. Ba(OH) 2 + H2SO4 → H2O + BaSO4 10. CaF2 + H2SO4 → CaSO4 + HF 

11. KClO3 → KClO4 + KCl 

2NaCl+ I2 → NaI + Cl2 2NaCl+ I2 → 

2NaI + Cl2 14.1

Name: Date: 

14.1 The Avogadro Number 

Atoms are so small that you could fit millions of them on the head of a pin. As you have learned, the masses of 

atoms and molecules are measured in atomic mass units. Working with atomic mass units in the laboratory is 

very difficult because each atomic mass unit has a mass of 1 / 12 the mass of one carbon atom. 

In order to make atomic mass units more useful, it would be convenient to relate the value of one atomic mass 

unit to one gram. One gram is an amount of matter we can actually see. For example, the mass of one paper clip 

is about 2.5 grams. The Avogadro number, 6.02 × 10 23 , allows us to convert atomic mass units to grams. 

What is a mole? 

In chemistry, the term “mole” does not refer to a furry animal that lives underground. In chemistry, a mole is 

quantity of something and is used just like we use the term “dozen.” One dozen is equal to 12. One mole is equal 

to 6.02 × 10 23 , or the Avogadro number. If you have a dozen oranges, you have 12. If you have a mole of 

oranges, you have 6.02 × 10 23 . This would be enough oranges to cover the entire surface of Earth seven feet deep 

in oranges! 

Could you work with only a dozen atoms in the laboratory? You cannot see 12 atoms without the aid of a very 

powerful microscope. A mole of atoms would be much easier to work with in the laboratory because the mass of 

one mole of atoms can be measured in grams. Moles allow us to convert atomic mass units to grams. This 

relationship is illustrated below: 

1 carbon atom = 12.0 amu 

To calculate the mass of one mole of any substance (the molar mass), you use the periodic table to find the 

atomic mass (not the mass number) for the element or for the elements that create the compound. You then 

express this value in grams. 

Substance Elements in 

substance 

Atomic 

mass of 

element 

(amu) 

No. of atoms of 

each element 

Formula mass 

(amu) 

Molar mass 

(g) 

Na Na 22.99 1 22.99 22.99 

U U 238.03 1 238.03 238.03 

H2O H 

1.01 

2 

18.02 18.02 

O 

16.00 

1 

CaCO3 Ca 40.08 

1 

100.09 100.09 

C 

12.01 

1 

O 

16.00 

3 

Al(NO3) 3 

213.01 213.01 

Al 

N 

O 

1 mole of carbon atoms 6.02 10 23 = × atoms = 

12.0 grams 

26.98 

14.01 

16.00 

1 

3 

9 

14.1

Page 2 of 4 

For the following elements and compounds, complete the following table to calculate the mass of one 

mole of the substance: 


substance 

Sr 

Ne 

Ca(OH) 2 

NaCl 

O 3 

C 6H 12O 

Atomic 

mass of 

element 

(amu) 

The molar mass of a substance can be used to calculate the number of particles (atoms or molecules) present in 

any given mass of a substance. You can determine the number of particles present by using the Avogadro 

number. 

Using the Avogadro number 

No. of atoms of 

each element 

The Avogadro number states that for one mole of any substance, whether element or compound, there are 

6.02 × 10 23 particles present in the sample. Those particles are atoms if the substance is an element and 

molecules if the substance is a compound. If we look again at our previous examples we see that every substance 

has a different molar mass: 

14.1 

Formula mass (amu) Molar mass 

(g)

Page 3 of 4 


substance 

Atomic 

mass of 

element 

(amu) 

No. of atoms 

of each 

element 

However, one mole of each of these substances contains exactly the same number of fundamental particles, 

6.02 × 10 23 . The difference is that each of these fundamental particles, atoms, and molecules, has a different 

mass based on its composition (number of protons and neutrons, numbers and types of atoms). Therefore, the 

number of particles in one mole of any substance is identical; however, the mass of one mole of substances varies 

based on the formula mass for that substance. 

When a substance’s mass is reported in grams and you need to find the number of particles present in the sample, 

you must first convert the mass in grams to the mass in moles. By using proportions and ratios, you can easily 

calculate the molar mass of any given amount of substance. 

How many molecules are in a sample of NaCl that has a mass of 38.9 grams? 

First, determine the molar mass of NaCl: 

Next, determine how many particles are in 38.9 g of NaCl: 

Formula mass 

(amu) 

Molar mass 

(g) 

Na Na 22.99 1 22.99 22.99 

U U 238.03 1 238.03 238.03 

H2O H 

1.01 

2 

18.02 18.02 

O 

16.00 

1 

CaCO3 Ca 40.08 

1 

100.09 100.09 

C 

12.01 

1 

O 

16.00 

3 

Al(NO3) 3 Al 

26.98 

1 

313.1 313.1 

N 

14.01 

3 

O 

16.00 

9 

Element Atomic mass (amu) No. of atoms Molar mass (g) 

Sodium (Na) 22.99 1 22.99 

Chlorine (Cl) 35.45 1 35.45 

Molar mass of NaCl 58.44 g 

We know that 58.44 g of NaCl contains 6.02 × 10 23 molecules of NaCl. Therefore, we can set up a proportion to 

determine the number of molecules in 38.9 g of NaCl: 

58.44 g NaCl 

6.02 10 23 

------------------------------- = 

× 

38.9 g NaCl 

---------------------------x 

Solving for x using cross-multiplication gives us a value of 4.0 × 10 23 molecules of NaCl. 

14.1

Page 4 of 4 

14.1 

Complete the following table by determining the molar mass of each listed substance and either 

providing the number of particles in the given mass of sample or the mass of the sample that contains the given 

number of particles. 

Substance Molar Mass 

(g) 

MgCO 3 

Mass of Sample 

(g) 

12.75 

Number of 

Particles Present 

H 2O 296 × 10 50 

N 2 

Yb 0.00038 

Al 2(SO 3) 3 

K 2CrO 4 

4657 

7.1 × 10 8 

0.23 × 10 19

Name: Date: 

14.1 Formula Mass 

A chemical formula gives you useful information about a compound. First, it tells you which types of atoms and 

how many of each are present. Second, it lets you know which types of ions are present in a compound. Finally, 

it allows you to determine the mass of one molecule of a compound, relative to the mass of other compounds. We 

call this the formula mass. This skill sheet will show you how to calculate the formula mass of a compound. 

Calculating formula mass: a step-by-step approach 

A common ingredient in toothpaste is a compound called sodium phosphate. If you examine a tube of toothpaste, 

you will find that it is usually listed as trisodium phosphate. 

• What is the formula mass of sodium phosphate? 

Step 1: Determine the formulas and oxidation numbers of the ions in the compound. 

Sodium phosphate is made up of the sodium ion and the phosphate ion. The oxidation number for the sodium ion 

can be determined from the periodic table. Since sodium, Na, is located in group 1 of the periodic table, it has an 

oxidation number of 1+ like all of the elements in group 1. 

The chemical formula and oxidation number for sodium is: Na + 

To find the formula and oxidation number for the phosphate ion, use the ion chart in Chapter 16 of your textbook. 

The chemical formula and oxidation number for the phosphate ion is: PO 4 3- 

Step 2: Write the chemical formula of the compound. 

Remember that compounds must be neutral that is, the oxidation numbers of the elements and ions must be equal 

to zero. Since sodium = Na + and phosphate = PO 4 3- how many of each do you need to make a neutral 

compound? You need three sodium ions for each phosphate ion to make a neutral compound. 

The chemical formula of sodium phosphate is: Na 3 PO 4 . 

Step 3: List the type of atom, quantity, atomic mass, and total mass of each atom. 

Atom Quantity Atomic mass 

(from the periodic table) 

Step 4: Add up the values and calculate the formula mass of the compound. 

68.97 amu + 30.97 amu + 64.00 amu = 163.94 amu 

The formula mass of sodium phosphate is 163.94 amu 

Total mass 

(number × atomic mass) 

Na 3 22.99 amu 3 × 22.99 = 68.97 amu 

P 1 30.97 amu 1 × 30.97 = 30.97 amu 

O 4 16.00 amu 4 × 16.00 = 64.00 amu 

14.1

Page 2 of 2 

Now try one on your own: 

Eggshells are made mostly of a brittle compound called calcium phosphate. What is the formula mass of this 

compound? 

1. Write the chemical formula and oxidation number of each ion in the compound: 

First ion: Second ion: 

2. Write the chemical formula of the compound: 

3. List the type of atom, quantity, atomic mass, and total mass of each atom. 


(from the periodic table) 

4. Add up the values to calculate the formula mass of the compound. 

Write the chemical formula and the formula mass for each of the compounds below. Use separate paper and show 

all of your work. 

1. barium chloride 

2. sodium hydrogen carbonate 

3. magnesium hydroxide 

4. ammonium nitrate 

5. strontium phosphate 

Total mass 

(number × atomic mass) 

14.1

Name: Date: 

14.2 Classifying Reactions 

Chemical reactions may be classified into different groups according to the reactants and products. The five 

major groups of chemical reactions are summarized below. 

Synthesis reactions - when two or more substances combine to form a new compound. 

• General equation: A + B → AB 

• Example: When rust forms, iron reacts with oxygen to form iron oxide (rust). 

4Fe (s) + 3O 2 (g) →2 Fe 2O 3 (s) 

Decomposition reactions - when a single compound is broken down to produce two or more smaller 

compounds. 

• General equation: AB → A + B 

• Example: Water can be broken down into hydrogen and oxygen gases. 

2H 2O (l) → 2H 2 (g) + O 2 (g) 

Single displacement reactions - when one element replaces a similar element in a compound. 

• General equation: A + BX → AX + B 

• Example: When iron is added to a solution of copper chloride, iron replaces copper in the solution and 

copper falls out of the solution. 

Fe (s) + CuCl 2 (aq) → Cu (s) + FeCl 2 (aq) 

Double displacement reactions - when ions from two compounds in solution exchange places to produce two 

new compounds. 

• General equation: AX + BY → AY + BX 

• Example: When carbon dioxide gas is bubbled into lime water, a precipitate of calcium carbonate is formed 

along with water. 

CO 2 (g) + CaO 2H 2 (aq) → CaCO 3 (s) + H 2O (l) 

Combustion reactions - when a carbon compound reacts with oxygen gas to produce carbon dioxide and water 

vapor. Energy is released from the reaction. 

• General equation: Carbon Compound + O2 → CO2 + H2O + energy 

• Example: The combustion of methane gas. 

CH 4 (g) + 2O 2 → CO 2 (g) + 2H 2O (g) 

Classify the following reaction as synthesis, decomposition, single displacement, double displacement, or 

combustion. Explain your answer. 

Mg (s) + CuSO 4 (s) → MgSO 4 (aq) + Cu (s) 

Answer: Displacement. Magnesium replaces copper in the compound. 

14.2

Page 2 of 2 

Classify the reactions below as synthesis, decomposition, single displacement, double 

displacement, or combustion. Explain your answers. 

1. CO 2 (g) + H 2O (l) → H 2CO 3 (aq) 

2. Cl 2 (g) + 2KI (aq) → 2KCl (aq) + I 2 (g) 

3. H 2O 2 (l) → H 2O (l) + O 2 (g) 

4. MnSO 4 (s) → MnO (s) + SO 3 (g) 

5. C 6H 12O 6 (s) + 6O 2 (g) → 6CO 2 (g) + 6H 2O (g) 

6. CaCl 2 (aq) + 2AgNO 3 (aq) → Ca(NO 3) 2 (aq) + 2AgCl (s) 

7. 2NaCl (aq) + CuSO 4 (aq) → Na 2SO 4 (aq) + CuCl 2 (s) 

8. CaCl 2 (aq) + 2Na (s) → Ca (s) + 2NaCl (aq) 

9. CaCO 3 (s) → CaO (s) + CO 2 (g) 

10. C 3H 8 (g) + 5O 2 (g) → 3CO 2 (g) + 4H 2O (g) 

Answer the following questions. 

11. You mix two clear solutions. Instantly, you see a bright yellow precipitate form. What type of reaction did 

you just observe? Explain your answer. 

12. What type of reaction occurs when you strike a match? 

13. Solid sodium reacts violently with chlorine gas. The product formed in the reaction is sodium chloride, also 

known as table salt. What type of reaction is this? Explain your answer. 

14. Hydrogen-powered cars burn hydrogen gas to produce water and energy. The reaction is: 

2H 2 (g) + O 2 (g) → 2H 2O (g) + Energy 

While this reaction can be classified as a synthesis reaction, it is sometimes referred to as combustion. What 

characteristics does this reaction share with other combustion reactions? How is it different? 

14.2

Name: Date: 

14.2 Predicting Chemical Equations 

Chemical reactions cause chemical changes. Elements and compounds enter into a reaction, and new substances 

are formed as a result. Often, we know the types of substances that entered the reaction and can tell what types of 

substance(s) were formed. Sometimes, though, it might be helpful if we could predict the products of the 

chemical reaction—know in advance what would be formed and how much of it would be produced. 

For certain chemical reactions, this is possible, using our knowledge of oxidation numbers, types of chemical 

reactions, and how equations are balanced. In this skill sheet, you will practice writing a complete balanced 

equation for chemical reactions when only the identities of the reactants are known. 

Review: Chemical equations 

Recall that chemical equations show the process of a chemical reaction. The equation reads from left to right with 

the reactants separated from the products by an arrow that indicates “yields” or “produces.” 

In the chemical equation: 

Two atoms of lithium combine with one molecule of barium chloride to yield two molecules of lithium chloride 

and one atom of barium. The equation fully describes the chemical change for this reaction. 

For reactions such as the one above, a single displacement reaction, we are often able to predict the products in 

advance and write a completely balanced equation for the chemical change. Here are the steps involved: 

1. Predict the replacements for the reaction. 

In single displacement reactions, one element is replaced by a similar element in a compound. The pattern for 

this replacement is easily predictable: if the element doing the replacing forms a positive ion, it replaces the 

element in the compound that forms a positive ion. If the substance doing the replacing forms a negative ion, it 

replaces the element in the compound that forms a negative ion. 

For the reaction described above, we could predict that the lithium would replace the barium in the compound 

barium chloride since both lithium and barium have positive oxidation numbers. The resulting product would 

pair lithium (1+) and chlorine (1-): the positive/negative combination required for ionic compounds. 

2. Determine the chemical formula for the products. 

Once you have determined which elements will be swapped to form the products, you can use oxidation numbers 

and the fact that the sum of the oxidation numbers for an ionic compound must equal zero in order to determine 

the chemical formula for the reaction products. 

3. Balance the chemical equation 

2Li + BaCl2 → 

2LiCl + Ba 

Once you have determined the nature and formulas of the products for a chemical reaction, the final step is to 

write a balanced equation for the reaction. 

14.2

Page 2 of 2 

• If beryllium (Be) combines with potassium iodide (KI) in a chemical reaction, what are the 

products? 

Solution: 

First, we decide which element of KI will be replaced by the beryllium. Since beryllium has an oxidation 

number of 2+, it replaces the element in KI that also has a positive oxidation number—the potassium (K 1+ ). 

It will therefore combine with the iodine to form a new compound. 

Because beryllium has an oxidation number of 2+ and iodine's oxidation number is 1–, it is necessary for 

two atoms of iodine to combine with one atom of beryllium to form an electrically neutral compound. The 

resulting chemical formula for beryllium iodide is BeI2. In single-displacement reactions, the component of the compound that has been replaced by the uncombined 

reactant now stands alone and uncombined. The resulting products of this chemical reaction, therefore, are 

BeI2 and K. Balancing the equation give us: 

Predict replacements 

Be + 2KI → BeI 2 + 2K 

1. If Na 1+ were to combine with CaCl 2, what component of CaCl 2 would be replaced by the Na 1+ ? 

2. If Fe 2+ were to combine with K 2Br, what component of K 2Br would be replaced by the Fe 2+ ? 

3. If Mg 2+ were to combine with AlCl 3, what component of AlCl 3 would be replaced by the Mg 2+ ? 

Predict product formulas 

For the following combinations of reactants, predict the formulas of the products: 

4. Li + AlCl 3 

5. K + CaO 

6. F 2 + KI 

Predicting chemical equations for displacement reactions 

Write complete balanced equations for the following combinations of reactants. 

7. Ca and K 2S 

8. Mg and Fe 2O 3 

9. Li and NaCl 

14.2

Name: Date: 

14.2 Percent Yield 

You can predict the amount of product to expect from a reaction if you know how much reactant you started with. 

For example, if you start out with one mole of limiting reactant, you can expect to produce one mole of product. 

In real-world chemical reactions, the actual amount of product is usually less than the predicted amount. This is 

due to experimental error and other factors (such as the fact that some product is difficult to collect and measure). 

The amount of product you expect to produce is called the predicted yield. The amount of product that you are 

able to measure after the reaction is called the actual yield. The percent yield is the actual yield divided by the 

predicted yield and then multiplied by 100. 

Actual yield 

Percent yield = 

----------------------------------- × 100 

Predicted yield 

The percent yield can provide information about how carefully the experiment was performed. If a percent yield 

is low, chemical engineers look for sources of error. Manufacturers of chemical products try to maximize their 

percent yield so that they can get the maximum amount of product to sell from the reactants that they purchased. 

I 

• In the reaction below, potassium and water are combined in a chemical reaction that produces potassium 

hydroxide and hydrogen gas. If two moles of potassium (the limiting reactant) are used, what is the predicted 

yield of potassium hydroxide (KOH) in grams? 

2K + 2H 2O → 2KOH + H 2 

1. Looking for: Predicted yield of KOH in grams 

2. Given: Two moles of the limiting reactant (K) are used 

3. Relationships: Two moles of limiting reactant should produce two moles of product. Two moles of 

the product will have a mass twice its molar mass. 

4. Solution: Molar mass of KOH = atomic mass of K + atomic mass of O + atomic mass of H 

From periodic table, molar mass of KOH = 39.10 + 16.00 + 1.01 = 56.11 grams 

Because we started with two moles of limiting reactant, we should end up with two 

moles, or 112.22 grams, of KOH. 

• If the actual yield of KOH was 102.5 grams, what was the percent yield for this reaction? 

1. Looking for: Percent yield of KOH 

2. Given: Actual yield = 102.5 g; predicted yield = 122.22 g 

3. Relationships: Percent yield = actual yield ÷ predicted yield × 100 

4. Solution: Percent yield = 102.5 g ÷ 112.22 g × 100 = 91.3% 

14.2

Page 2 of 2 

1. In the balanced reaction below, hydrochloric acid reacts with calcium carbonate to produce calcium 

chloride, carbon dioxide, and water. 

2HCL + CaCO 3 → CaCl 2 + CO 2 + H 2O 

If one mole of calcium carbonate (the limiting reactant) is used, how much calcium chloride should the 

reaction produce? Give your answer in grams. (Hint: use your periodic table to find the atomic masses of 

calcium and chlorine). 

2. If the actual yield of calcium chloride in the reaction is 97.6 grams, what is the percent yield? 

3. In order to get a 94% actual yield for this reaction, how many grams of calcium chloride would the reaction 

need to produce? 

4. If you put an iron nail into a beaker of copper (II) chloride, you will begin to see a reddish precipitate 

forming on the nail. In this reaction, iron replaces copper in the solution and copper falls out of the solution 

as a metal. Here is the balanced reaction: 

Fe + CuCl 2 → FeCl 2 + Cu 

If you start out with one mole of your limiting reactant (Fe), how many grams of copper can you expect to 

produce through this reaction? 

5. If the actual yield of copper in the reaction is 55.9 grams, what is the percent yield? 

6. How much copper would the reaction need to produce to achieve a 96% yield? 

7. When sodium hydroxide and sulfuric acid react, sodium sulfate and water are produced. Here is the balanced 

reaction: 

2NaOH + H 2SO 4 → NaSO 4 + 2H 2O 

If two moles of sodium hydroxide (the limiting reactant) are used, one mole of NaSO 4 should be produced. 

How many grams of NaSO 4 should be produced? 

8. If 100.0 grams of NaSO 4 are actually produced, what is the percent yield? 

9. How much NaSO 4 would have to be produced to achieve a 90% yield? 

10. Name two reasons why the actual yield in a reaction is usually lower than the predicted yield. 

14.2

Name: Date: 

14.4 Lise Meitner 

Lise Meitner identified and explained nuclear fission, proving it was possible to split an atom. 

Prepared to learn 

allowed to attend. 

Lise Meitner was born in 

Vienna on November 7, 

1878, one of eight children; 

her father was among the first 

Jews to practice law in 

Austria. At 13, she completed 

the schooling provided to 

girls. Her father hired a tutor 

to help her prepare for a 

university education, 

although women were not yet 

The preparation was worthwhile. When the University 

of Vienna opened its doors to women in 1901, Meitner 

was ready. She found a mentor there in physics 

professor Ludwig Boltzmann, who encouraged her to 

pursue a doctoral degree. Physicist Otto Robert Frisch, 

Meitner’s nephew, wrote that “Boltzmann gave her the 

vision of physics as a battle for ultimate truth, a vision 

she never lost.” 

Pioneer in radioactivity 

In 1906 Meitner went to Berlin after earning her 

doctorate, only the second in physics awarded to a 

woman by the university. There was great interest in 

theoretical physics in Berlin. There she began a 

30-year collaboration with chemist Otto Hahn. 

Together, they studied radioactive substances. One of 

their first successes was the development of a new 

technique for purifying radioactive material. 

During World War I, Meitner volunteered as an X-ray 

nurse-technician with the Austrian army. She 

pioneered cautious handling techniques for 

radioactive substances, and when she was off duty, 

continued her work with Hahn. 

Elemental discoveries 

In 1917, they discovered the element protactinium. 

Afterward, Meitner was appointed head of the physics 

department at the Kaiser Wilhelm Institute for 

Chemistry in Berlin, where Hahn was head of the 

chemistry department. The two continued their study 

of radioactivity, and Meitner became the first to 

explain how conversion electrons were produced 

when gamma rays were used to remove orbital 

electrons. 

Atomic-age puzzles 

14.4 

In 1934, when Enrico Fermi produced radioactive 

isotopes of uranium by neutron bombardment, he was 

puzzled by the products. Meitner, Hahn, and German 

chemist Fritz Strassmann began looking for answers. 

Their research was interrupted when Nazi Germany 

annexed Austria in 1938 and restrictions on “non- 

Aryan” academics tightened. Meitner, though she had 

been baptized and raised a Protestant, went into exile 

in Sweden. She continued to correspond with her 

collaborators and suggested that they perform further 

tests on a product of the uranium bombardment. 

When tests showed it was barium, the group was 

puzzled. Barium was so much smaller than uranium. 

Hahn wrote to Meitner that uranium “can’t really 

break into barium … try to think of some other 

possible explanation.” 

Meitner and Frisch (who was also in Sweden) worked 

on the problem and proved that splitting the uranium 

atom was energetically possible. Using Neils Bohr’s 

model of the nucleus, they explained how the neutron 

bombardment could cause the nucleus to elongate into 

a dumbbell shape. Occasionally, they explained, the 

narrow center of the dumbbell could separate, leaving 

two nuclei. Meitner and Frisch called this process 

nuclear fission. 

Meitnerium honors achievement 

In 1944, Hahn received the Nobel Prize in chemistry 

for the discovery of nuclear fission. Meitner’s role was 

overlooked or obscured. 

In 1966, she, Hahn, and Strassman shared the Enrico 

Fermi Award, given by President Lyndon B. Johnson 

and the Department of Energy. Meitner died two years 

later, just days before her 90th birthday. In 1992, 

element 109 was named meitnerium to honor her 

work.

Page 2 of 2 


1. Research: Ludwig Boltzmann was an important mentor to Lise Meitner. Who was Boltzmann? 

Research and list one of his contributions to science. 

2. What element did Meitner and Otto Hahn discover? Using the periodic table, list the atomic number and 

mass number of this element. Does this element have stable isotopes? 

3. What is nuclear fission? Explain this event in your own words and draw a diagram showing how fission 

occurs in a uranium nucleus. 

4. Research and describe at least two ways nuclear fission was used in the twentieth century. 

5. Meitner did not receive the Nobel Prize for her work on nuclear fission, though she was honored in other 

ways. List how she was honored for her work in physics. 

6. On a separate sheet of paper, compose a letter to the Nobel Prize Committee explaining why Meitner 

deserved this prize for her work. Be sure to explain your reasoning clearly and be sure to use formal 

language and correct grammar in your letter. 

14.4

Name: Date: 

14.4 Marie and Pierre Curie 

14.4 

Marie and Pierre Curie’s pioneering studies of radioactivity had a dramatic impact on the development 

of twentieth-century science. Marie Curie’s bold view that uranium rays seemed to be an intrinsic part of uranium 

atoms encouraged physicists to explore the possibility that atoms might have an internal structure. Out of this 

idea the field of nuclear physics was born. Together the Curies discovered two radioactive elements, polonium 

and radium. Through Pierre Curie’s study of how living tissue responds to radiation, a new era in cancer 

treatment was born. 

The allure of learning 

Marya Sklodowska was born 

on November 7, 1867, in 

Russian-occupied Warsaw, 

Poland. She was the 

youngest of five children of 

two teachers, her father a 

teacher of physics and 

mathematics, her mother 

also a singer and pianist. 

Marya loved school, and especially liked math and 

science. However, in Poland, as in much of the rest of 

the world, opportunities for higher education were 

limited for women. At 17, she and one of her sisters 

enrolled in an illegal, underground “floating 

university” in Warsaw. 

After these studies, she worked for three years as a 

governess. Her employer allowed her to teach reading 

to the children of peasant workers at his beet-sugar 

factory. This was forbidden under Russian rule. At the 

same time, she took chemistry lessons from the 

factory’s chemist, mathematics lessons from her father 

by mail, and studied on her own. 

By fall 1891, Sklodowska had saved enough money to 

enroll at the University of Paris (also called the 

Sorbonne). She earned two master’s degrees, in 

physics and mathematics. 

A Polish friend introduced Marie, as she was called in 

French, to Pierre Curie, the laboratory chief at the 

Sorbonne’s Physics and Industrial Chemistry Schools. 

The piezoelectric effect 

Pierre Curie’s early research 

centered on properties of 

crystals. He and his brother 

Jacques discovered the 

piezoelectric effect, which 

describes how a crystal will 

oscillate when electric 

current is applied. The 

oscillation of crystals is now 

used to precisely control 

timing in computers and watches and many other 

devices. 

Pierre Curie and Marie Sklodowska found that despite 

their different nationalities and background, they had 

the same passion for scientific research and shared the 

desire to use their discoveries to promote 

humanitarian causes. They married in 1895. 

Crystals and uranium rays 

Pierre continued his pioneering research in crystal 

structures, while Marie pursued a physics doctorate. 

She chose uranium rays as her research topic. 

Uranium rays had been discovered only recently by 

French physicist Henri Becquerel. 

Becquerel’s report explained that uranium compounds 

emitted some sort of ray that fogged photographic 

plates. Marie Curie decided to research the effect these 

rays had on the air’s ability to conduct electricity. To 

measure this effect, she adapted a device that Pierre 

and Jacques Curie had invented 15 years earlier.

Page 2 of 3 

Marie Curie confirmed that the electrical effects of 

uranium rays were similar to the photographic effects 

that Becquerel reported—both were present whether 

the uranium was solid or powdered, pure or in 

compound, wet or dry, exposed to heat or to light. 

She concluded that the emission of rays by uranium 

was not the product of a chemical reaction, but could 

be something built into the very structure of uranium 

atoms. 

Allies behind a revolutionary idea 

Marie Curie’s idea was revolutionary because atoms 

were still believed to be tiny, featureless particles. She 

decided to test every known element to see if any 

others would, like uranium, improve the air’s ability to 

conduct electricity. She found that the element 

thorium had this property. 

Pierre Curie decided to join Marie after she found that 

two different uranium ores (raw materials gathered 

from uranium mines) caused the air to conduct 

electricity much better than even pure uranium or 

thorium. They wondered if an undiscovered element 

might be mixed into each ore. 

They worked to separate the chemicals in the ores and 

found two substances that were responsible for the 

increased conductivity. They called these elements 

polonium, in honor of Marie’s native country, and 

radium, from the Greek word for ray. 

A new field of medicine 

While Marie Curie searched for ways to extract these 

pure elements from the ores, Pierre turned his 

attention to the properties of the rays themselves. He 

tested the radiation on his own skin and found that it 

damaged living tissue. 

As Pierre published his findings, a whole new field of 

medicine developed, using targeted rays to destroy 

cancerous tumors and cure skin diseases. 

Unfortunately, both Curies became ill from 

overexposure to radiation. 

Curies share the Nobel Prize 

In June 1903, Madame Curie became the first woman 

in Europe to receive a doctorate in science. In 

December of that year, the Curies and Becquerel 

shared the Nobel Prize in physics. 

The Curies were honored for their work on 

the spontaneous radiation that Becquerel had 

14.4 

discovered. Marie Curie called spontaneous 

radiation “radioactivity.” She was the first woman to 

win the Nobel in physics. And in 1904, her second 

daughter, Eve, was born. The elder daughter, Irene, 

was seven. 

Tragedy intrudes 

In April 1906, Pierre was killed by a horse-drawn 

wagon in a Paris street accident. A month later, the 

Sorbonne asked Madame Curie to take over her 

husband’s position there. She agreed, in hopes of 

creating a state-of-the art research center in her 

husband’s memory. 

Marie Curie threw herself into the busy academic 

schedule of teaching and conducting research (she was 

the first woman to lecture, the first to be named 

professor, and the first to head a laboratory at the 

Sorbonne), and found time to work on raising money 

for the new center. The Radium Institute of the 

University of Paris opened in 1914 and Madame Curie 

was named director of its Curie Laboratory. 

The scientist-humanitarian 

In 1911, Curie received a second Nobel Prize (the first 

person so honored), this time in chemistry for her 

work in finding elements and determining the atomic 

weight of radium. 

With the start of World War I in 1914, she turned her 

attention to the use of radiation to help wounded 

soldiers. Assisted by her daughter Irene, she created a 

fleet of 20 mobile x-ray units to help medics quickly 

determine and then treat injuries in the field. Next, she 

set up nearly 200 x-ray labs in hospitals and trained 

150 women to operate the equipment. 

Legacy continues 

After the war, Curie went back to direct the Radium 

Institute, which grew to two centers, one devoted to 

research and the other to treatment of cancer. In July 

1934, she died at 66 of radiation-induced leukemia. 

The next year, Irene Joliot-Curie and her husband, 

Frederic Joliot-Curie, were awarded the Nobel Prize in 

chemistry for their discovery of artificial radiation.

Page 3 of 3 


1. Why might Marie Curie have been motivated to teach the children of beet workers? Recall that this 

was forbidden by Russian rule. 

2. What fundamental change in our understanding of the atom was brought about by the work of Marie Curie? 

3. Describe how Marie and Pierre Curie discovered two elements. 

4. Name at least three new fields of science that stem from the work of Marie and/or Pierre Curie. 

5. Research: In your own words, describe Marie Curie as a role model for women in science. Use your library 

or the Internet to research how she worked to balance a scientific career and motherhood. 

14.4

Name: Date: 

14.4 Rosalyn Sussman Yalow 

14.4 

Rosalyn Sussman Yalow and her research partner, Solomon Berson, developed radioimmunoassay, or 

RIA. This important medical diagnostic tool uses radioactive isotopes to trace hormones, enzymes, and 

medicines that exist in such low concentrations in blood that they were previously impossible to detect using 

other laboratory methods. 

Encouraged and inspired 

Rosalyn Sussman was born in 

1921 in New York City. 

Neither of her parents 

attended school beyond eighth 

grade, but they encouraged 

Rosalyn and her older brother 

to value education. In the early 

grades, Rosalyn enjoyed math, 

but in high school her 

chemistry teacher encouraged 

her interest in science. 

She stayed in New York after high school, studying 

physics and chemistry at Hunter College. After her 

graduation in 1941, she took a job as a secretary at 

Columbia University. There were few opportunities 

for women to attend graduate school, and Sussman 

hoped that by working at Columbia, she might be able 

to sit in on some courses. 

A wartime opportunity 

However, as the United States began drafting large 

numbers of men in preparation for war, universities 

began to accept women rather than close down. In fall 

1941, Sussman arrived at the University of Illinois 

with a teaching assistantship in the School of 

Engineering, where she was the only woman. 

There, she specialized in the construction and use of 

devices for measuring radioactive substances. By 

January 1945 she had earned her doctorate, with 

honors, in nuclear physics, and married Aaron Yalow, 

a fellow student. 

From medical physics to ‘radioimmunoassay’ 

From 1946–50, Yalow taught physics at Hunter 

College, which had only introduced it as a major her 

senior year and which now admitted men. In 1947, she 

also began working part time at the Veterans 

Administration Hospital in the Bronx, which was 

researching medical uses of radioactive substances. 

In 1950 she joined the hospital full time and began a 

research partnership with Solomon A. Berson, an 

internist. Together they developed the basic science, 

instruments, and mathematical analysis necessary to 

use radioactive isotopes to measure tiny 

concentrations of biological substances and certain 

drugs in blood and other body fluids. They called their 

technique radioimmunoassay, or RIA. (Yalow also had 

two children by 1954.) 

RIA helps diabetes research 

One early application of RIA was in diabetes research, 

which was especially significant to Yalow because her 

husband was diabetic. Diabetes is a condition in which 

the body is unable to regulate blood sugar levels. This 

is normally accomplished through the release of a 

hormone called insulin from the pancreas. 

Using RIA, they showed that adult diabetics did not 

always lack insulin in their blood, and that, therefore, 

something must be blocking their insulin’s normal 

action. They also studied the body’s immune system 

response to insulin injected into the bloodstream. 

Commercial applications, not commerce 

RIA’s current uses include screening donated blood, 

determining effective doses of medicines, detecting 

foreign substances in the blood, testing hormone 

levels in infertile couples, and treating certain children 

with growth hormones. 

Yalow and Berson changed theoretical immunology 

and could have made their fortunes had they chosen to 

patent RIA, but instead, Yalow explained, “Patents are 

about keeping things away from people for the 

purpose of making money. We wanted others to be 

able to use RIA.” Berson died unexpectedly in 1972; 

Yalow had their VA research laboratory named after 

him, and lamented later that his death had excluded 

him from sharing the team’s greatest recognition. 

A rare Nobel winner 

Yalow was awarded the Nobel Prize in Physiology or 

Medicine in 1977. She was only the second woman to 

win in that category, for her work on radioimmunoassay 

of peptide hormones.

Page 2 of 2 


1. Rosalyn Yalow has said that Eve Curie’s biography of her mother, Marie Curie, helped spark her 

interest in science. Compare the lives of these two scientists. 

2. Describe radioimmunoassay in your own words. 

3. What information about adult diabetes was discovered using RIA? 

4. Find out more about the role of patents in medical research. Do you agree or disagree with Yalow’s 

statement? Why? 

14.4

Name: Date: 

14.4 Chien-Shiung Wu 

14.4 

During World War II, Chinese-American physicist Chien-Shiung Wu played an important role in the 

Manhattan Project, the Army’s secret work to develop the atomic bomb. In 1957, she overthrew what was 

considered an indisputable law of physics, changing the way we understand the weak nuclear force. 

Determined to learn 

Chien-Shiung Wu was born on 

May 31, 1912, in a small town 

outside Shanghai, China. Her 

father had opened the region’s 

first school for young girls, 

which Chien-Shiung finished 

at age 10. 

She then attended a girls 

boarding school in Suzhou 

that had two sections—a 

teacher training school and an academic school with a 

standard Western curriculum. Chien-Shiung enrolled 

in teacher training, because tuition was free and 

graduates were guaranteed jobs. 

Students from both sections lived in the dormitory, 

and as Chien-Shiung became friends with girls in the 

academic school, she learned that their science and 

math curriculum was more rigorous than hers. She 

asked to borrow their books and stayed up late 

teaching herself the material. 

Chien-Shiung Wu graduated first in her class and was 

invited to attend prestigious National Central 

University in Nanjing. There, she earned a bachelor’s 

degree in physics and did research for two years. In 

1936 Wu emigrated from China to the United States. 

She earned her doctorate from the University of 

California at Berkeley in 1940. 

A key scientist in the Manhattan Project 

Wu taught at Smith College and Princeton University 

until 1944, when she went to Columbia University as a 

senior scientist and researcher and was asked to join 

the Manhattan Project. There she helped develop the 

process to enrich uranium ore. 

In the course of the project, her renowned colleague 

Enrico Fermi turned to Wu for help with a fission 

experiment. A rare gas which she had studied in 

graduate school was causing the problem. With Wu’s 

assistance, Fermi was able to solve the problem and 

continue his work. 

Right and left in nature? 

After the war, Wu continued her research in nuclear 

physics at Columbia. In 1956, she and two colleagues, 

Tsung-Dao Lee of Columbia and Chen Ning Yang of 

Princeton, reconsidered the law of conservation of 

parity. This law stated that nature does not distinguish 

between left and right in nuclear reactions. They 

wondered if the law might not be valid for interactions 

of subatomic particles involving the weak nuclear 

force. 

Wu was a leading specialist in beta decay. She figured 

out a means of testing their theory. She cooled cobalt- 

60, a radioactive isotope, to 0.01 degree above 

absolute zero. Next, she placed the cobalt-60 in a 

strong magnetic field so that the cobalt nuclei lined up 

and spun along the same axis. She observed what 

happened as the cobalt-60 broke down and gave off 

electrons. 

According to the law of conservation of parity, equal 

numbers of electrons should have been given off in 

each direction. However, Wu found that many more 

electrons flew off in the direction opposite the spin of 

the cobalt-60 nuclei. She proved that in beta decay, 

nature does in fact distinguish between left and right. 

Always a landmark achiever 

Unfortunately, when Lee and Yang were awarded the 

Nobel Prize in physics in 1957, Wu’s contribution to 

the project was overlooked. However, among her 

many honors and awards, she later received the 

National Medal of Science, the nation’s highest award 

for science achievement. 

In 1973, she became the first female president of the 

American Physical Society. Wu died at 84 in 1997, 

leaving a husband and son who were both physicists.

Page 2 of 2 


1. Use a dictionary to look up the meaning of each boldface word. Write a definition for each word. 

Be sure to credit your source. 

2. How did Chien-Shiung Wu’s work in graduate school help her with her work on the Manhattan Project? 

3. From the reading, define the law of conservation of parity in your own words. 

4. How many protons and neutrons does cobalt-60 have? List the nonradioactive isotopes of cobalt. 

5. Briefly describe Wu’s elegant experiment that proved that nature distinguishes between right and left. 

6. Research: Wu was the first woman recipient of the National Medal of Science in physical science. Two 

other women have since received this award. Who were they and what did they do? 

7. What are three questions that you have about Wu and her work? 

8. Suggest some possible reasons why Wu did not receive the Nobel Prize for her work. 

14.4

Name: Date: 

14.4 Radioactivity 

There are three main types of radiation that involve the decay of the nucleus of an atom: 

• alpha radiation (α): release of a helium-4 nucleus (two protons and two neutrons). We can represent 

4 

helium-4 using isotope notation: 2He 

. The top number, 4, represents the mass number, and the bottom 

number represents the atomic number for helium, 2. 

• beta radiation (β): release of an electron. 

• gamma radiation (γ): release of an electromagnetic wave. 

Half-life 

The time it takes for half of the atoms in a sample to decay is called the half-life. Four kilograms of a certain 

substance undergo radioactive decay. Let’s calculate the amount of substance left over after 1, 2, and 3 half-lives. 

• After one half-life, the substance will be reduced by half, to 2 kilograms. 

• After two half-lives, the substance will be reduced by another half, to 1 kilogram. 

• After three half-lives, the substance will be reduced by another half, to 0.5 kilogram. 

So, if we start with a sample of mass m that decays, after a few half-lives, the mass of the sample will be: 

Number of half-lives Mass left 

1 ----m 

1 

= 

2 1 

2 ----m 

1 

= 

2 2 

3 ----m 

1 

= 

2 3 

4 ----m 

1 

= 

2 4 

1 

--m 

2 

1 

--m 

4 

1 

--m 

8 

-----m 

1 

16 

14.4

Page 2 of 2 

1. The decay series for uranium-238 and plutonium-240 are listed below. Above each arrow, write “a” 

for alpha decay or “b” for beta decay to indicate which type of decay took place at each step. 

a. 238 → 234 → 234 → 234 → 230 → 

92 U 

226 

88 Ra 

214 

84 Po 

240 

94 Pu 

90 Th 

222 

86 Rn 

210 

82 Pb 

91 Pa 

218 

84 Po 

→ → → → → 

210 

83 Bi 

→ → → → 

240 

95Am 236 

93 Np 

b. → → → → → 

228 

90 Bi 

212 

83 Bi 

224 

88 Ra 

224 

89 Ac 

→ → → → → 

212 

84 Po 

208 

82 Pb 

→ → → 

18 

92 U 

214 

82 Pb 

210 

84 Po 

232 

91 Pa 

220 

87 Fr 

208 

83 Bi 

90 Th 

214 

83 Bi 

206 

82 Pb 

232 

92 U 

216 

85 At 

2. Fluorine-18 ( 9F 

) has a half-life of 110 seconds. This material is used extensively in medicine. The hospital 

18 

laboratory starts the day at 9 a.m. with 10 grams of 9F 

. 

a. How many half-lives for fluorine-18 occur in 11 minutes (660 seconds)? 

b. How much of the 10-gram sample of fluorine-18 would be left after 11 minutes? 

14 

3. The isotope 6C 

has a half-life of 5,730 years. What is the fraction of 6C 

in a sample with mass, m, after 

28,650 years? 

4. What is the half-life of this radioactive isotope that decreases to one-fourth its original amount in 18 months? 

5. This diagram illustrates a formula that is used to calculate the intensity of radiation from a radioactive 

source. Radiation “radiates” from a source into a spherical area. Therefore, you can calculate intensity using 

the area of a sphere ( 4πr ). Use the formula and the diagram to help you answer the questions below. 

2 

a. A radiation source with a power of 1,000. watts is located at a point in space. What is the intensity of 

radiation at a distance of 10. meters from the source? 

b. The fusion reaction releases 2.8 × 10 –12 2 

1H 

H 

joules of energy. How many such 

reactions must occur every second in order to light a 100-watt light bulb? Note that one watt equals one 

joule per second. 

3 4 

+ 1 → 

2He + n + energy 

14 

14.4

Page 1 of 2 

15.2 Svante Arrhenius 

15.2 

Svante Arrhenius was a Swedish Chemist who won the Nobel Prize in 1903 for his work on acid and 

base chemistry. He is also known for recognizing that carbon dioxide (CO2 ) is added to the atmosphere when 

fossil fuels are burned, and that it is a greenhouse gas. Arrhenius calculated that doubling the CO2 in the 

atmosphere would increase Earth’s temperature by 4-5°C. His prediction, made without computers or modern 

scientific equipment, is close to current estimates! 

Young scholar 

Svante Arrhenius was born in 

1859 in Wijk, Sweden. His 

father was a land surveyor. 

Svante taught himself to read 

at the age of three. He was a 

strong student and especially 

enjoyed math and physics. He 

graduated at the top of his high 

school class, although he was 

the youngest student. 

Arrhenius went on to study 

mathematics, chemistry, and physics at the University of 

Uppsala in Sweden. In 1881 he moved to Stockholm to 

study with Professor E. Edlund at the Academy of 

Sciences. Arrhenius was especially interested in what 

happens when electricity is passed through solutions. For 

his doctoral thesis, he proposed that molecules in solutions 

could break up into electrically charged fragments called 

ions. 

Setback, perseverance, and recognition 

Unfortunately, the value of Arhenius’s work was not 

recognized by the faculty at the University of Uppsala, 

where he defended his dissertation. The idea that a 

molecule could break up in water was difficult to accept. 

Finally, Arrhenius was given a “fourth rank” degree--which 

meant that he barely passed. Arrhenius could not hope to 

obtain a university professorship with that degree! 

Arrhenius’s mentor, Professor Edlund, helped him obtain a 

travel grant to meet and work with leading scientists in the 

field of physical chemistry. They helped Arrhenius clarify 

his ionic theory. In the late 1890’s, when electrically 

charged subatomic particles were discovered, the 

importance of Arrhenius’s work was finally recognized. 

Arrhenius was awarded the Nobel Prize for Chemistry in 

1903. 

A man of many interests 

Arrhenius was fascinated by many branches of science. He 

studied electrolytes in the human body, publishing papers 

about their role in digestion and absorption, and about their 

function as antitoxins. 

Along with his scientific publications, Arrhenius wrote 

books intended to introduce the general public to advances 

in various scientific fields. These included Smallpox and its 

Combating (1913) and Chemistry and Modern Life (1919). 

Arrhenius was also interested in Astronomy. In 1908 he put 

forth the theory of panspermy--which suggested that life 

may spread through the universe when spores from a lifebearing 

planet escape their atmosphere and are then driven 

by radiation pressure across long expanses of space, until 

they come to rest on another planet where hospitable 

conditions allow them to flourish. While this theory hasn’t 

withstood the test of time, Arrhenius did contribute to our 

understanding of the phenomenon known as Aurora 

Borealis, or northern lights. 

Pioneering climate research 

Arrhenius was curious about what caused the beginning 

and end of Earth’s ice ages. In 1895, he presented a paper 

to the Stockholm Physical Society called “On the Influence 

of Carbonic Acid (CO2 ) in the Air upon the Temperature of 

the Ground.” He proposed that variations in the amount of 

CO2 in the atmosphere could influence climate. 

In 1903, he wrote a book called Worlds in the Making in 

which he explained that atmospheric gases like carbon 

dioxide trap heat near Earth’s surface, increasing its 

average temperature. In 1904, he suggested that human 

activity could affect Earth’s climate, if industrial emissions 

increased the amount of CO2 in the atmosphere. He was not 

concerned about this increase; in fact he thought that it 

might be beneficial for growing crops to feed a larger 

human population. 

Arrhenius died in Stockholm in 1927.

Page 2 of 2 


1. Describe Arrhenius’s doctoral thesis. 

2. What was the setback that Arrhenius had to overcome early in his career? 

3. Name three fields of science that interested Arrhenius. 

4. Describe a scientific theory proposed by Arrhenius that has never received widespread acceptance. 

5. Why is Arrhenius considered a pioneer in the field of climate change study? 

15.2

Name: Date: 

16.1 Open and Closed Circuits 

Where is the current flowing? 

You have built and tested different kinds of circuits in the lab. Now you can use what you learned to make 

predictions about circuits you haven’t seen before. Use the circuit diagrams pictured below to answer the 

questions. You may wish to write on the diagrams in order to keep track where the current is flowing. As a result, 

each diagram is repeated several times. 

1. Which devices (A, B, C, or D) in the circuit pictured below will be on when the following conditions are 

met? For your answer, give the letter of the device or devices. 

a. Switch 3 is open, and all other switches are closed. 

b. Switch 2 is open, and all other switches are closed. 

c. Switch 4 is open, and all other switches are closed. 

d. Switch 1 is open, and all other switches are closed. 

e. Bulb C blows out, and all switches are closed. 

f. Bulb A blows out, and all switches are closed. 

. 

g. Switches 2 and 4 are open, and switches 1 and 3 are closed. 

h. Switches 2 and 3 are open, and switches 1 and 4 are closed. 

16.1

. 

Page 2 of 3 

i. Switches 2, 3, and 4 are open, and switch 1 is closed. 

j. Switches 1 and 2 are open, and switches 3 and 4 are closed. 

2. Which of the devices (A-G) in the circuit below will be on when the following conditions are met? For your 

answer, give the letter of the device or devices. 

a. Switch 5 is open, and all other switches are closed. 

b. Switch 6 is open, and all others are closed. 

c. Switch 7 is open, and all others are closed. 

. 

d. Switch 4 is open, and all others are closed. 

e. Switch 3 is open, and all others are closed. 

f. Switch 2 is open, and all others are closed. 

g. Switch 1 is open, and all others are closed. 

h. Switches 2 and 4 are open, and all others are closed. 

16.1

. 

Page 3 of 3 

i. Switches 4 and 6 are open, and all others are closed. 

j. Switches 4 and 7 are open, and all others are closed. 

k. Switches 5 and 7 are open, and all others are closed. 

l. Switches 2 and 3 are open, and all others are closed. 

m. Bulb D blows out with all switches closed. 

n. Bulbs A and B blow out with all switches closed. 

o. Bulbs A and D blow out with all switches closed. 

3. Use arrows to draw the direction of the current in each of the circuits below. Make sure to show current 

direction in all paths of the circuits within each diagram. 

4. How many possible paths are there in circuit diagrams in questions (1) and (2)? 

5. Draw a circuit of your own. Use one battery, show at least 4 devices (bulbs and bells), and divide the current 

at some point in the circuit. Finally, use arrows to show the direction of the current in all parts of your circuit. 

16.1

Name: Date: 

16.1 Benjamin Franklin 

Benjamin Franklin overcame a lack of formal education to become a prominent businessman, 

community leader, inventor, scientist, and statesman. His study of “electric fire” changed our basic 

understanding of how electricity works. 

An eye toward inventiveness 

Benjamin Franklin was born 

in Boston in 1706. With only 

one year of schooling he 

became an avid reader and 

writer. He was apprenticed at 

age 12 to his brother James, a 

printer. The siblings did not 

always see eye to eye, and at 

17, Ben ran away to 

Philadelphia. 

In his new city, Franklin developed his own printing 

and publishing business. Over the years, he became a 

community leader, starting the first library, fire 

department, hospital, and fire insurance company. He 

loved gadgets and invented some of his own: the 

Franklin stove, the glass armonica (a musical 

instrument), bifocal eyeglasses, and swim fins. 

‘Electric fire’ 

In 1746, Franklin saw some demonstrations of static 

electricity that were meant for entertainment. He 

became determined to figure out how this so-called 

“electric fire” worked. 

Undeterred by his lack of science education, Franklin 

began experimenting. He generated static electricity 

using a glass rod and silk cloth, and then recorded how 

the charge could attract and repel lightweight objects. 

Franklin read everything he could about this “electric 

fire” and became convinced that a lightning bolt was a 

large-scale example of the same phenomenon. 

Father and son experiment 

In June 1752, Franklin and his 21-year-old son, 

William, conducted an experiment to test his theory. 

Although there is some debate over the details, most 

historians agree that Franklin flew a kite on a stormy 

day in order to collect static charges. 

16.1 

Franklin explained that he and his son constructed a 

kite of silk cloth and two cedar strips. They attached a 

metal wire to the top. Hemp string was used to fly the 

kite. A key was tied near the string’s lower end. A silk 

ribbon was affixed to the hemp, below the key. 

Shocking results 

It is probable that Franklin and his son were under 

some sort of shelter, to keep the silk ribbon dry. They 

got the kite flying, and once it was high in the sky they 

held onto it by the dry silk ribbon, not the wet hemp 

string. Nothing happened for a while. Then they 

noticed that the loose threads of the hemp suddenly 

stood straight up. 

The kite probably was not struck directly by lightning, 

but instead collected charge from the clouds. Franklin 

touched his knuckle to the key and received a static 

electric shock. He had proved that lightning was a 

discharge of static electricity. 

Those are charged words 

Through his experiments, Franklin determined that 

“electric fire” was a single “fluid” rather than two 

separate fluids, as European scientists had thought. 

He proposed that this “fluid” existed in two states, 

which he called “positive” and “negative.” Franklin 

was the first to explain that if there is an excess 

buildup of charge on one item, such as a glass rod, it 

must be exactly balanced by a lack of charge on 

another item, such as the silk cloth. Therefore, electric 

charge is conserved. He also explained that when there 

is a discharge of static electricity between two items, 

the charges become balanced again. 

Many of Franklin’s electrical terms remain in use 

today, including battery, charge, discharge, electric 

shock, condenser, conductor, plus and minus, and 

positive and negative.

Page 2 of 2 


1. Although Ben Franklin had only one year of schooling, he became a highly educated person. 

Describe how Franklin learned about the world. 

2. What hypothesis did Franklin test with his kite experiment? 

3. Describe the results and conclusion of Franklin’s kite experiment. 

4. Franklin’s kite experiment was dangerous. Explain why. 

5. Silk has an affinity for electrons. When you rub a glass rod with silk, the glass is left with a positive charge. 

Make a diagram that shows the direction that charges move in this example. Illustrate and label positive and 

negative charges on the silk and glass rod in your diagram. Note: Show the same number of positive and 

negative charges in your diagram. 

6. Research: Among Franklin’s many inventions is the lightning rod. Find out how this device works, and 

create a model or diagram to show how it functions. 

16.1

Name: Date: 

16.2 Using an Electric Meter 

What do you measure in a circuit and how do you measure it? This skill sheet gives you useful tips to help you 

use an electric meter and understand electrical measurements. 

The digital multimeter 

Most people who work with electric circuits use a digital multimeter to measure electrical quantities. These 

measurements help them analyze circuits. Most multimeters measure voltage, current, and resistance. A typical 

multimeter is shown below: 

16.2

Page 2 of 4 

Using the digital multimeter 

This table summarizes how to use and interpret any digital meter in a battery circuit. Note: A component 

is any part of a circuit, such as a battery, a bulb, or a wire. 

Measuring Voltage Measuring Current Measuring Resistance 

Circuit is ON Circuit is ON Circuit is OFF 

Turn dial to voltage, labeled Turn dial to current, labeled Turn dial to resistance, labeled Ω 

Connect leads to meter following 

meter instructions 

Place leads at each end of 

component (leads are ACROSS 

the component) 



Break circuit and place leads on 

each side of the break (meter is IN 

the circuit) 



Place leads at each end of 

component (leads are ACROSS 

the component) 

Measurement in VOLTS (V) Measurement in AMPS (A) Measurement in OHMS (Ω) 

Battery measurement shows 

relative energy provided 

Component measurement shows 

relative energy used by that 

component 

Measurement shows the value of 

current at the point where meter is 

placed 

Current is the flow of charge 

through the wire 

Measurement shows the 

resistance of the component 

When the resistance is too high, 

the display shows OL (overload) 

or ∝ (infinity) 

16.2

Page 3 of 4 

Build a series circuit with 2 batteries and 2 bulbs. 

1. Measure and record the voltage across each battery: 

2. Measure and record the voltage across each bulb: 

3. Measure and record the voltage across both batteries: 

4. Draw a circuit diagram or sketch that shows all the posts in the circuit (posts are where wires and holders 

connect together). 

5. Break the circuit at one post. Measure the current and record the value below. Repeat until you have 

measured the current at every post. 

16.2

Page 4 of 4 

6. Create a set of instructions on how to use the meter to do a task. Find someone unfamiliar with the 

meter. See if he or she can follow your instructions. 

7. A fuse breaks a circuit when current is too high. A fuse must be replaced when it breaks a circuit. Explain 

how measuring the resistance of a fuse can tell you if it is defective. 

8. You suspect that a wire is defective but can't see a break in it. Explain how measuring the resistance of the 

wire can tell you if it has a break. 

16.2

Name: Date: 

16.3 Voltage, Current, and Resistance 

Electricity is one of the most fascinating topics in physical science. It’s also one of the most useful to understand, 

since we all use electricity daily. This skill sheet reviews some of the important terms in the study of electricity. 

In the reading section, you’ll find questions that check your understanding. If you’re not sure of the answer, go 

back and read that section again. In the practice section, you will have an opportunity to show that you know how 

voltage, current, and resistance are related in real-world situations. 

What is voltage? 

What is current? 

16.3 

You know that water will flow from a higher tank through a hose into a 

lower tank. The water in the higher tank has greater potential energy than the 

water in the lower tank. A similar thing happens with the flow of charges in 

an electric circuit. 

Charges flow in a circuit when there is a difference in energy level from one 

end of the battery (or any other energy source) to the other. This energy 

difference is measured in volts. The energy difference causes the charges to 

move from a higher to a lower voltage in a closed circuit. 

Think of voltage as the amount of “push” the electrical source supplies to the 

circuit. A meter is used to measure the amount of energy difference or 

“push” in a circuit. The meter reads the voltage difference (in volts) between 

the positive and the negative ends of the power source (the battery). This 

voltage difference supplies the energy to make charges flow in a circuit. 

1.What is the difference between placing a 1.5-volt battery in a circuit and 

placing a 9-volt battery in a circuit? 

Current describes the flow of electric charges. Current is the actual measure of how many charges are flowing 

through the circuit in a certain amount of time. Current is measured in units called amperes. 

Just as the rate of water flowing out of a faucet can be fast or slow, electrical current can move at different rates. 

The type, length, and thickness of wire all effect how much current flows in a circuit. Resistors slow the flow of 

current. Adding voltage causes the current to speed up. 

2. What could you do to a closed circuit consisting of a battery, a light bulb, and a switch that would increase 

the amount of current? Explain your answer. 

3. What could you do to a closed circuit consisting of a battery, a light bulb, and a switch that would decrease 

the amount of current? Explain your answer.

Page 2 of 3 

What is resistance? 

16.3 

Resistance is the measure of how easily charges flow through a circuit. High resistance means it is 

difficult for charges to flow. Low resistance means it is easy for charges to flow. Electrical resistance is measured 

in units called ohms (abbreviated with the symbol Ω). 

Resistors are items that reduce the flow of charge in a circuit. They act like “speed bumps” in a circuit. A light 

bulb is an example of a resistor. 

4. Describe one thing that you could do to the wire used in a circuit to decrease the amount of resistance 

presented by the wire. 

How are voltage, current, and resistance related? 

When the voltage (push) increases, the current (flow of charges) will also increase, and when the voltage 

decreases, the current likewise decreases. These two variables, voltage and current, are said to be directly 

proportional. 

When the resistance in an electric circuit increases, the flow of charges (current) decreases. These two variables, 

resistance and current, are said to be inversely proportional. When one goes up, the other goes down, and vice 

versa. 

The law that relates these three variables is called Ohm’s Law. The formula is: 

Voltage (volts) 

Current (amps) = 

Resistance (ohms, Ω) 

5. In your own words, state the relationship between resistance and current, as well as the relationship between 

voltage and current. 

• In a circuit, how many amps of current flow through a resistor such as a 6-ohm light bulb when using four 

1.5-volt batteries as an energy supply? 

Solution: 

4× 1.5 volts 6 volts 

Current = 

= 

6 ohms 6 ohms 

Current = 1 amp

Page 3 of 3 

Now you will have the opportunity to demonstrate your understanding of the relationship between current, 

voltage and resistance. Answer each of the following questions and show your work. 

1. How many amps of current flow through a circuit that includes a 9-volt battery and a bulb with a resistance 

of 6 ohms? 

2. How many amps of current flow through a circuit that includes a 9-volt battery and a bulb with a resistance 

of 12 ohms? 

3. How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms of 

resistance? 

4. How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 amps? 

16.3

Name: Date: 

16.3 Ohm’s Law 

A German physicist, Georg S. Ohm, developed this mathematical relationship, known as Ohm’s Law, which is 

present in most circuits. It states that if the voltage in a circuit increases, so does the current. If the resistance 

increases, the current decreases. 

To work through this skill sheet, you will need the symbols used to depict circuits in 

diagrams. The symbols that are most commonly used for circuit diagrams are 

provided to the right. 

If a circuit contains more than one battery, the total voltage is the sum of the 

individual voltages. A circuit containing two 6 V batteries has a total voltage of 12 V. 

[Note: The batteries must be connected positive to negative for the voltages to add.] 

• If a toaster produces 12 ohms of resistance in a 120-volt circuit, what is the 

amount of current in the circuit? 

Solution: 

The current in the toaster circuit is 10 amps. 




V 120 volts 

I = = = 10 amps 

R 12 ohms 

Note: If a problem asks you to calculate the voltage or resistance, you must rearrange the equation to solve 

for V or R. All three forms of the equation are listed below. 

V V 

I = V = IR R = 

R I 

Answer the following question using Ohm’s law. Don’t forget to show your work. 

1. How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 3 ohms? 

2. How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 12 ohms? 

3. A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current. 

4. A circuit contains two 1.5 volt batteries and a bulb with a resistance of 3 ohms. Calculate the current. 

5. What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance? 

6. A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb? 

16.3

Page 2 of 2 

7. How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms 

of resistance? 

8. How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 

amps? 

9. An alarm clock draws 0.5 A of current when connected to a 120 volt circuit. Calculate its resistance. 

10. A portable CD player uses two 1.5 V batteries. If the current in the CD player is 2 A, what is its resistance? 

11. You have a large flashlight that takes 4 D-cell batteries. If the current in the flashlight is 2 amps, what is the 

resistance of the light bulb? (Hint: A D-cell battery has 1.5 volts.) 

12. Use the diagram below to answer the following problems. 

a. What is the total voltage in each circuit? 

b. How much current would be measured in each circuit if the light bulb has a resistance of 6 ohms? 

c. How much current would be measured in each circuit if the light bulb has a resistance of 12 ohms? 

d. Is the bulb brighter in circuit A or circuit B? Why? 

13. What happens to the current in a circuit if a 1.5-volt battery is removed and is replaced by a 9-volt battery? 

14. In your own words, state the relationship between resistance and current in a circuit. 

15. In your own words, state the relationship between voltage and current in a circuit. 

16. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to increase the 

current? Explain your answer. 

17. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to decrease the 

current? Explain your answer. 

18. You have four 1.5 V batteries, a 1 Ω bulb, a 2 Ω bulb, and a 3 Ω bulb. Draw a circuit you could build to 

create each of the following currents. There may be more than one possible answer for each. 

a. 1 ampere 

b. 2 amperes 

c. 3 amperes 

d. 6 amperes 

16.3

Name: Date: 

16.4 Series Circuits 

In a series circuit, current follows only one path from the positive end of the battery toward the negative end. The 

total resistance of a series circuit is equal to the sum of the individual resistances. The amount of energy used by 

a series circuit must equal the energy supplied by the battery. In this way, electrical circuits follow the law of 

conservation of energy. Understanding these facts will help you solve problems that deal with series circuits. 

To answer the questions in the practice section, you will have to use Ohm’s law. Remember that: 




Some questions ask you to calculate a voltage drop. We often say that each resistor (or light bulb) creates a 

separate voltage drop. As current flows along a series circuit, each resistor uses up some energy. As a result, the 

voltage gets lower after each resistor. If you know the current in the circuit and the resistance of a particular 

resistor, you can calculate the voltage drop using Ohm’s law. 

Voltage drop across resistor (volts) = 

Current through resistor (amps) × Resistance of one resistor (ohms) 

1. Use the series circuit pictured to the right to answer 

questions (a)–(e). 

a. What is the total voltage across the bulbs? 

b. What is the total resistance of the circuit? 

c. What is the current in the circuit? 

d. What is the voltage drop across each light bulb? 

(Remember that voltage drop is calculated by 

multiplying current in the circuit by the resistance of a 

particular resistor: V = IR.) 

e. Draw the path of the current on the diagram. 

2. Use the series circuit pictured to the right to answer 

questions (a)–(e). 

a. What is the total voltage across the bulbs? 





3. What happens to the current in a series circuit as more light bulbs are added? Why? 

4. What happens to the brightness of each bulb in a series circuit as additional bulbs are added? Why? 

16.4

Page 2 of 2 

5. Use the series circuit pictured to the right to 

answer questions (a), (b), and (c). 

a. What is the total resistance of the circuit? 

b. What is the current in the circuit? 

c. What is the voltage drop across each resistor? 

6. Use the series circuit pictured to the right to 

answer questions (a)–(e). 

a. What is the total voltage of the circuit? 





7. Use the series circuit pictured right to answer questions 

(a), (b), and (c). Consider each resistor equal to all others. 

a. What is the resistance of each resistor? 

b. What is the voltage drop across each resistor? 

c. On the diagram, show the amount of voltage in the 

circuit before and after each resistor. 

8. Use the series circuit pictured right to answer questions 

(a)–(d). 

a. What is the total resistance of the circuit? 


c. What is the voltage drop across each resistor? 

d. What is the sum of the voltage drops across the three 

resistors? What do you notice about this sum? 

9. Use the diagram to the right to answer 

questions (a), (b), and (c). 

a. How much current would be measured 

in each circuit if each light bulb has a 

resistance of 6 ohms? 

b. How much current would be measured 

in each circuit if each light bulb has a 

resistance of 12 ohms? 

c. What happens to the amount of current 

in a series circuit as the number of 

batteries increases? 

16.4

Name: Date: 

16.4 Parallel Circuits 

A parallel circuit has at least one point where the circuit divides, creating more than one path for current. Each 

path is called a branch. The current through a branch is called branch current. If current flows into a branch in a 

circuit, the same amount of current must flow out again. This rule is known as Kirchoff’s current law. 

Because each branch in a parallel circuit has its own path to the battery, the voltage across each branch is equal to 

the battery’s voltage. If you know the resistance and voltage of a branch you can calculate the current with Ohm’s 

Law (I = V/R). 

1. Use the parallel circuit pictured right to answer 

questions (a)–(d). 

a. What is the voltage across each bulb? 

b. What is the current in each branch? 

c. What is the total current provided by the battery? 

d. Use the total current and the total voltage to 

calculate the total resistance of the circuit. 



a. What is the voltage across each bulb? 


c. What is the total current provided by the battery? 

d. Use the total current and the total voltage to 

calculate the total resistance of the circuit. 



a. What is the voltage across each resistor? 


c. What is the total current provided by the 

batteries? 

d. Use the total current and the total voltage to calculate the total resistance of the circuit. 


questions (a)–(c). 

a. What is the voltage across each resistor? 


c. What is the total current provided by the 

battery? 

16.4

Page 2 of 2 

In part (d) of problems 1, 2, and 3, you calculated the total resistance of each circuit. This required you to first 

find the current in each branch. Then you found the total current and used Ohm’s law to calculate the total 

resistance. Another way to find the total resistance of two parallel resistors is to use the formula shown below. 

Calculate the total resistance of a circuit containing two 6 ohm resistors. 

Given 

The circuit contains two 6 Ω resistors in parallel. 

Looking for 

The total resistance of the circuit. 

Relationships 

R 

total 

1. Calculate the total resistance of a circuit containing each of the following combinations of resistors. 

a. Two 8 Ω resistors in parallel 

b. Two 12 Ω resistors in parallel 

c. A 4 Ω resistor and an 8 Ω resistor in parallel 

d. A 12 Ω resistor and a 3 Ω resistor in parallel 

2. To find the total resistance of three resistors A, B, and C in parallel, first use the formula to find the total of 

resistors A and B. Then use the formula again to combine resistor C with the total of A and B. Use this 

method to find the total resistance of a circuit containing each of the following combinations of resistors. 

a. Three 8 Ω resistors in parallel 

= 

R × R 

R + 

R 

1 2 

1 2 

total 

b. Two 6 Ω resistors and a 2 Ω resistor in parallel 

c. A 1 Ω, a 2 Ω, and a 3 Ω resistor in parallel 

R 

= 

R × R 

R + R 

1 2 

1 2 

Solution 

R 

R 

total 

total 

6 Ω× 6 Ω 

= 

6 Ω+ 6 Ω 

= 3 Ω 

The total resistance is 3 ohms. 

16.4

Name: Date: 

16.4 Thomas Edison 

16.4 

Thomas Alva Edison holds the record for the most patents issued to an individual in the United States: 

1,093. He is famous for saying that “Genius is one percent inspiration and ninety-nine percent perspiration.” 

Edison’s hard work and imagination brought us the phonograph, practical incandescent lighting, motion pictures, 

and the alkaline storage battery. 

The young entrepreneur 

Thomas Alva Edison was born 

February 11, 1847, in Milan, Ohio, the 

youngest of seven children. His family 

moved to Port Huron, Michigan, in 

1854 and Thomas attended school 

there—for a few months. He was 

taught reading, writing, and simple arithmetic by his 

mother, a former teacher, and he read widely and 

voraciously. The basement was his first laboratory. 

When he was 13, Thomas started selling newspapers 

and candy on the train from Port Huron to Detroit. 

Waiting for the return train, he often read science and 

technology books. He set up a chemistry lab in an 

empty boxcar, until he accidentally set the car on fire. 

At 16, Thomas learned to be a telegraph operator and 

began to travel the country for work. His interest in 

experiments and gadgets grew and he invented an 

automatic timer to send telegraph messages while he 

slept. About this time his hearing was deteriorating; he 

was left with only about 20 percent hearing in one ear. 

First a patent, then business 

In 1868 Edison arrived in Boston. His first patent was 

issued there for an electronic vote recorder. While the 

device worked very well, it was a commercial failure. 

Edison vowed that, in the future, he would only invent 

things he was certain the public would want. 

He moved on to New York, where he invented a 

“Universal Stock Printer” for which he was paid 

$40,000, a huge sum he found hard to comprehend. 

After developing some devices to improve telegraph 

communications, Edison had enough money to build a 

research lab in Menlo Park, New Jersey. 

The invention factory 

Edison’s facility had everything he needed for 

inventing: machine and carpentry shops, a lab, offices, 

and a library. He hired assistants who specialized 

where he felt he was lacking, in mathematics, for 

instance. 

The concept of a commercial research facility—an 

“invention factory” of sorts—was new. Some consider 

Menlo Park itself to be one of Edison’s most important 

inventions. 

It was there Edison invented the tin foil phonograph, 

the first machine to record and play back sounds. 

Next, he developed a practical, safe, and affordable 

incandescent light. The company he formed to 

manufacture and market this invention eventually 

became General Electric. 

In 1888, Edison opened an even larger research 

complex in West Orange, New Jersey. Here he 

improved the phonograph and created a device that 

“does for the eye what the phonograph does for the 

ear.” This was the first motion picture player. 

Not a man to be discouraged 

Not all of Edison’s ideas were successful. In the 1890s 

he sold all his stock in General Electric and invested 

millions to develop better methods of mining iron ore. 

He never was able to come up with a workable process 

and the investment was a loss. 

One of the most remarkable aspects of Edison’s 

character was his refusal to be discouraged by failure. 

The 3,500 notebooks he kept illustrate his typical 

approach to inventing: brainstorm as many avenues as 

possible to create a product, try anything that seems 

remotely workable, and record everything. Failed 

experiments, he said, helped direct his thinking toward 

more useful designs. 

Edison also worked to create an efficient storage 

battery to use in electric cars. By the time his alkaline 

battery was ready, electric cars were uncommon. But 

the invention proved useful in other devices, like 

lighting railway cars and miners’ lamps. Edison’s last 

patent was granted when he was 83, the year before he 

died, and his last big undertaking was an attempt, at 

Henry Ford’s request, to develop an alternative source 

of rubber. He was still working on the project when he 

died in 1931.

Page 2 of 2 


1. Name three different avenues by which Thomas Edison received an education. 

2. What did Edison learn from his attempts to sell his first patented invention? 

3. Describe Edison’s “invention factory.” 

4. Name two important inventions that came out of Menlo Park. 

5. Describe the process Edison used to invent things. 

6. How did Edison view his projects that failed? 

7. How do you think the tin foil phonograph worked? Discuss and compare your ideas with a fellow member of 

your class. 

8. Research: Edison holds the record for the most patents issued to an individual in the United States. Use a 

library or the Internet to research three of his inventions that are not mentioned in this biography, and briefly 

describe each one. 

16.4

Page 1 of 2 

16.4 George Westinghouse 

16.4 

George Westinghouse was both an imaginative tinkerer and a bold entrepreneur. His inventions had a 

profound effect on nineteenth-century transportation and industrial development in the United States. His air 

brakes and signaling systems made railway systems safer at higher speeds, so that railroads became a 

practical method of transporting goods across the country. He promoted alternating current as the best means of 

providing electric power to businesses and homes, and his method became the worldwide standard. 

Westinghouse obtained 361 patents over the course of his life. 

A boyhood among machines 

George Westinghouse was born 

October 6, 1846, in Central Bridge, 

New York. When he was 10, his family 

moved to Schenectady, where his 

father opened a shop that 

manufactured agricultural machinery. 

George spent a great deal of time working and 

tinkering there. 

After serving in both the Union Army and Navy in the 

Civil War, Westinghouse attended college for three 

months. He dropped out after receiving his first patent 

in 1865, for a rotary steam engine he had invented in 

his father’s shop. 

An inventive train of thought 

In 1866, Westinghouse was aboard a train that had to 

come to a sudden halt to avoid colliding with a 

wrecked train. To stop the train, brakemen manually 

applied brakes to each individual car based on a signal 

from the engineer. 

Westinghouse believed there could be a safer way to 

stop these heavy trains. In April 1869, he patented an 

air brake that enabled the engineer to stop all the cars 

in tandem. That July he founded the Westinghouse Air 

Brake Company, and soon his brakes were used by 

most of the world’s railways. 

The new braking system made it possible for trains to 

travel safely at much higher speeds. Westinghouse 

next turned his attention to improving railway 

signaling and switching systems. Combining his own 

inventions with others, he created the Union Switch 

and Signal Company. 

Long-distance electricity 

Next, Westinghouse became interested in transmitting 

electricity over long distances. He saw the potential 

benefits of providing electric power to individual 

homes and businesses, and in 1884 formed the 

Westinghouse Electric Company. Westinghouse 

learned that Nikola Tesla had developed alternating 

current and he persuaded Tesla to join the company. 

Initially, Westinghouse met with resistance from 

Thomas Edison and others who argued that direct 

current was a safer alternative. But direct current 

could not be transmitted over distances longer than 

three miles. Westinghouse demonstrated the potential 

of alternating current by lighting the streets of 

Pittsburgh, Pennsylvania, and, in 1893, the entire 

Chicago World’s Fair. Afterward, alternating current 

became the standard means of transmitting electricity. 

From waterfalls to elevated railway 

Also in 1893, Westinghouse began yet another new 

project: the construction of three hydroelectric 

generators to harness the power of Niagara Falls on 

the New York-Canada border. By November 1895, 

electricity generated there was being used to power 

industries in Buffalo, some 20 miles away. 

Another Westinghouse interest was alternating current 

locomotives. He introduced this new technology first 

in 1905 with the Manhattan Elevated Railway in New 

York City, and later with the city’s subway system. 

An always inquiring mind 

The financial panic of 1907 caused Westinghouse to 

lose control of his companies. He spent much of his 

last years in public service. Westinghouse died in 1914 

and left a legacy of 361 patents in his name—the final 

one received four years after his death.

Page 2 of 2 


1. Where did George Westinghouse first develop his talent for inventing things? 

2. How did Westinghouse make it possible for trains to travel more safely at higher speeds? 

3. Why did Westinghouse promote alternating current over direct current for delivering electricity to 

businesses and homes? 

4. How did Westinghouse turn public opinion in favor of alternating current? 

5. Together with a partner, explain the difference between direct and alternating current. Write your 

explanation as a short paragraph and include a diagram. 

6. How did Westinghouse provide electrical power to the city of Buffalo, New York? 

7. Ordinary trains in Westinghouse’s time were coal-powered steam engines. How were Westinghouse’s 

Manhattan elevated trains different? 

8. Research: Westinghouse had a total of 361 patents to his name. Use a library or the Internet to find out about 

three inventions not mentioned in this brief biography, and describe each one. 

16.4

Name: Date: 

16.4 Lewis Latimer 

16.4 

Latimer, often called a “Renaissance Man,” was an accomplished African-American inventor receiving 

seven U.S. patents. His professional and personal achievements define him as a humanitarian, artist, and scientist. 

Son of former slaves 

Lewis Howard Latimer 

was born on September 4, 

1848 in Chelsea, 

Massachusetts. Latimer's 

parents had escaped from 

slavery in Virginia and 

moved north. In Boston, 

Latimer's father, George, 

was arrested and jailed 

because he was considered 

a fugitive. The 

Massachusetts Supreme Court ruled that he belonged 

to his owner in Virginia. 

The people of Boston protested and local supporters 

paid for his release. George was free. George and his 

wife settled in Chelsea where they started their family. 

In 1858, George, fearing he would be forced to return 

to slavery, went into hiding, leaving his family behind. 

Young Lewis Latimer attended grammar school in 

Chelsea and was a high-achieving student. As a 

teenager, Lewis lied about his age to join the Union 

Navy during the Civil War. After four years of military 

service, the war ended and Latimer was honorably 

discharged. 

Drafting a career 

Latimer looked for work in Boston and finally found a 

job as an office boy with a patent law firm, Crosby and 

Gould. He earned $3.00 per week. At the firm, Lewis 

studied the detailed patent drawings prepared by the 

draftsmen. Over time, he taught himself the drafting 

trade using the tools and books available there. 

Latimer showed his drawings to his boss and secured a 

job as a draftsman earning $20.00 per week. He 

eventually became chief draftsman and worked at the 

firm for eleven years. 

During this time, Latimer created patent drawings for 

Alexander Graham Bell. He completed the drawings 

and submitted them only hours before a competing 

inventor. Bell was awarded the telephone patent in 

1876 due to Latimer's hard work and drafting skills. 

An enlightened inventor 

Latimer was not only a talented draftsman, but also a 

successful inventor. While at Crosby and Gould, he 

developed his first invention—mechanical improvements 

for railroad train water closets (also known as toilets!). 

After Crosby and Gould, Latimer worked as a 

draftsman at the Follandsbee Machine Shop. Here he 

met Hiram Maxim and was hired to work at Maxim's 

company, U.S. Electric Lighting. Maxim was an 

inventor searching for ways to improve Thomas 

Edison’s light bulb. Edison held the patent for the light 

bulb, but the life span of the bulb was very short. 

Maxim wanted to extend the life of the light bulb and 

turned to Latimer for help. 

Latimer taught himself the details of electricity. In 

1881, he invented carbon filaments to replace paper 

filaments in light bulbs. He then went on to improve 

the manufacturing process for carbon filaments. Now 

light bulbs lasted longer, were more affordable, and 

had more uses. Latimer oversaw the installation of 

electric street lights in North America and London. He 

became chief electrical engineer for U.S. Electric 

Lighting and supervised The Maxim-Westin Electric 

Lighting Company in London. 

Edison and beyond 

In 1885, Thomas Edison hired Latimer to work in the 

legal department of Edison Electric Light Company. 

Latimer was the chief draftsman and patent authority 

working to protect Edison's patents. He wrote the 

widely acclaimed electrical engineering book called 

Incandescent Electric Lighting: A Practical 

Description of the Edison System. Latimer became one 

of only 28 members of the “Edison Pioneers” and the 

only African-American member. The Edison Pioneers 

were the most highly regarded men in the electrical 

field. Edison's company eventually became the 

General Electric Company. 

Latimer’s additional inventions included an early 

version of the air conditioner; a locking rack for hats, 

coats, and umbrellas; and a book support. He was also a 

poet, musician, playwright, painter, civil rights activist, 

husband, and father. Latimer died in 1928 at age 80.

Page 2 of 2 


1. How did Lewis Latimer become a draftsman and electrical engineer? 

2. List Latimer's major inventions. What was his most important invention and why? 

3. Research: What is a “Renaissance man”? Why is Latimer referred to as a Renaissance man? 

4. Research: Latimer was an accomplished poet. Locate and identify the names of two of his poems. 

5. Research: When did the Edison Pioneers first meet? Locate an excerpt from the obituary published by the 

Edison Pioneers honoring Lewis Latimer. 

16.4

Name: Date: 

17.1 Magnetic Earth 

Earth’s magnetic field is very weak compared with the strength of the field on the surface of the ceramic magnets 

you probably have in your classroom. The gauss is a unit used to measure the strength of a magnetic field. A 

small ceramic permanent magnet has a field of a few hundred up to 1,000 gauss at its surface. At Earth’s surface, 

the magnetic field averages about 0.5 gauss. Of course, the field is much stronger nearer to the core of the planet. 

1. What is the source of Earth’s magnetic field according to what you have read in chapter 17? 

2. Today, Earth’s magnetic field is losing approximately 7 percent of its strength every 100 years. If the 

strength of Earth’s magnetic field at its surface is 0.5 gauss today, what will it be 100 years from now? 

3. Describe what you think might happen if Earth’s magnetic field continues to lose strength. 

4. The graphic to the right illustrates one piece of evidence that proves the 

reversal of Earth’s poles during the past millions of years. The ‘crust’ of 

Earth is a layer of rock that covers Earth’s surface. There are two kinds of 

crust—continental and oceanic. Oceanic crust is made continually (but 

slowly) as magma from Earth’s interior erupts at the surface. Newly formed 

crust is near the site of eruption and older crust is at a distance from the site. 

Based on what you know about magnetism, why might oceanic crust rock 

be a record of the reversal of Earth’s magnetic field? (HINT: What happens 

to materials when they are exposed to a magnetic field?) 

5. The terms magnetic south pole and geographic north pole refer to locations 

on Earth. If you think of Earth as a giant bar magnet, the magnetic south 

pole is the point on Earth’s surface above the south end of the magnet. The 

geographic north pole is the point where Earth’s axis of rotation intersects 

its surface in the northern hemisphere. Explain these terms by answering the 

following questions. 

a. Are the locations of the magnetic south pole and the geographic north 

pole near Antarctica or the Arctic? 

b. How far is the magnetic south pole from the geographic north pole? 

c. In your own words, define the difference between the magnetic south pole and the geographic north 

pole. 

6. A compass is a magnet and Earth is a magnet. How does the magnetism of a compass work with the 

magnetism of Earth so that a compass is a useful tool for navigating? 

17.1

Page 2 of 2 

7. The directions—north, east, south, and west—are arranged on a compass so that they align with 

360 degrees. This means that zero degrees (0°) and 360° both represent north. For each of the 

following directions by degrees, write down the direction in words. The first one is done for you. 

a. 45° Answer: The direction is northeast. 

b. 180° 

c. 270° 

d. 90° 

e. 135° 

f. 315° 

Magnetic declination 

Earth’s geographic north pole (true north) and magnetic south pole are located near each other, but they are not at 

the same exact location. Because a compass needle is attracted to the magnetic south pole, it points slightly east 

or west of true north. The angle between the direction a compass points and the direction of the geographic north 

pole is called magnetic declination. Magnetic declination is measured in degrees and is indicated on 

topographical maps. 

8. Let’s say you were hiking in the woods and relying on a map and compass to navigate. What would happen 

if you didn’t correct your compass for magnetic declination? 

9. Are there places on Earth where magnetic declination equals 0°? Use the Internet or your local library to find 

out where on Earth there is no magnetic declination. 

17.1

Name: Date: 

17.2 Model Maglev Train Project 

Magnetically levitating (Maglev) trains use electromagnetic force to lift the 

train above the tracks. This system greatly reduces wear because there are few 

moving parts that carry heavy loads. It’s also more fuel efficient, since the 

energy needed to overcome friction is greatly reduced. Although maglev 

technology is still in its experimental stages, many engineers believe it will 

become the standard for mass transit systems over the next 100 years. 

This project will give you an opportunity to create a model maglev train. You 

can even experiment with different means of providing power to your train. 

Materials 

• 52 one-inch square magnets with north and south poles on the faces, rather than ends (found at hobby shops) 

• One strip of 1/4-inch thick foam core, 24 inches long by 4 inches wide 

• Two strips of 1/4-inch thick foam core, 24 inches long by 2.5 inches wide 

• One strip of 1/4-inch thick foam core, 6 inches long by 3.75 inches wide 

• Hot melt glue and glue gun 

• Masking tape 

Directions 

1. Cut a strip of masking tape 24 inches long. Press a line of 24 magnets onto the tape, north sides up. 

2. Hold an additional magnet north side down and run it along the strip to make sure that the entire “track” will 

repel the magnet. Flip over any magnets that attract your test magnet. 

3. Glue the magnet strip along one long side of the 24-by-4-inch foam core rectangle. 

4. Repeat steps 1-2, then glue the 

second magnet strip along the 

opposite side to create the other 

track. 

5. Place a bead of hot glue along the 

cut edge and attach one 24-by-2.5 

inch foam core rectangle to form a 

short wall. 

17.2

Page 2 of 2 

6. Repeat step 5 to form the opposite wall. This keeps the train from sliding sideways off the track. 

7. To create your train, glue the south side of a magnet to each corner of the small foam core rectangle. 

8. Turn the train over so that the north side of its magnets face the tracks. Place your train above the track and 

watch what happens! 

Extensions: 

1. Experiment with various means to propel your train along the tracks. Consider using balloons, rubber bands 

and toy propellers, small motors (available at hobby stores) or even jet propulsion using vinegar and baking 

soda as fuel. 

2. Build a longer, more permanent track using plywood shelving. Use clear, flexible plastic for the front wall so 

that you can see the train floating above the track. 

3. Find out how much weight your train can carry. Are some propulsion systems able to carry more weight than 

others? Why? 

4. Have a design contest to see who can build the fastest train, or the train that can carry the most weight from 

one end of the track to the other. 

17.2

Name: Date: 

17.4 Michael Faraday 

17.4 

Despite little formal schooling, Michael Faraday rose to become one of England’s top research 

scientists of the nineteenth century. He is best known for his discovery of electromagnetic induction, which made 

possible the large-scale production of electricity in power plants. 

Reading his way to a job 

Michael Faraday was born 

on September 22, 1791, in 

Surrey, England, the son of 

a blacksmith. His family 

moved to London, where 

Michael received a 

rudimentary education at a 

local school. 

At 14, he was apprenticed 

to a bookbinder. He enjoyed 

reading the materials he 

was asked to bind, and found himself mesmerized by 

scientific papers that outlined new discoveries. 

A wealthy client of the bookbinder noticed this 

voracious reader and gave him tickets to hear 

Humphry Davy, the British chemist who had 

discovered potassium and sodium, give a series of 

lectures to the public. 

Faraday took detailed notes at each lecture. He bound 

the notes and sent them to Davy, asking him for a job. 

In 1812, Davy hired him as a chemistry laboratory 

assistant at the Royal Institution, London’s top 

scientific research facility. 

Despite his lack of formal training in science or math, 

Faraday was an able assistant and soon began 

independent research in his spare time. In the early 

1820s, he discovered how to liquefy chlorine and 

became the first to isolate benzene, an organic solvent 

with many commercial uses. 

The first electric motor 

Faraday also was interested in electricity and 

magnetism. After reading about the work of Hans 

Christian Oersted, the Danish physicist, chemist, and 

electromagnetist, he repeated Oersted’s experiments 

and used what he learned to build a machine that used 

an electromagnet to cause rotation—the first electric 

motor. 

Next, he tried to do the opposite, to use a moving 

magnet to cause an electric current. In 1831, he 

succeeded. Faraday’s discovery is called 

electromagnetic induction, and it is used by power 

plants to generate electricity even today. 

The Faraday effect 

Faraday first developed the concept of a field to 

describe magnetic and electric forces, and used iron 

filings to demonstrate magnetic field lines. He also 

conducted important research in electrolysis and 

invented a voltmeter. 

Faraday was interested in finding a connection 

between magnetism and light. In 1845 he discovered 

that a strong magnetic field could rotate the plane of 

polarized light. Today this is known as the Faraday 

effect. 

A scientist’s public education 

Faraday was a teacher as well as a researcher. When 

he became director of the Royal Institution laboratory 

in 1825, he instituted a popular series of Friday 

Evening Discourses. Here paying guests (including 

Prince Albert, who was Queen Victoria’s husband) 

were entertained with demonstrations of the latest 

discoveries in science. 

A series of lectures on the chemistry and physics of 

flames, titled “The Natural History of a Candle,” was 

among the original Christmas Lectures for Children, 

which continue to this day. 

Named in his honor 

Faraday continued his work at the Royal Institution 

until just a few years before his death in 1867. Two 

units of measure have been named in his honor: the 

farad, a unit of capacitance, and the faraday, a unit of 

charge.

Page 2 of 2 


1. What did Michael Faraday do to get a job with Humphry Davy? Why was this effort important in 

getting Faraday started in science? 

2. Research benzene and list two modern-day commercial uses for this chemical. 

3. Based on the reading, define electromagnetic induction. 

4. In your own words, describe the Faraday effect. In your description, explain the term “polarized light.” 

5. How did Faraday contribute to society during his time as the director of the Royal Institution laboratory? 

6. Name two ways in which Faraday’s work affects your own life in the twenty-first century. 

7. Imagine you could go back in time to see one of Faraday’s demonstrations. Explain why you would like to 

attend one of his demonstrations. 

8. Activity: Use iron filings and a magnet to demonstrate magnetic field lines, or prepare a simple 

demonstration of electromagnetic induction for your classmates. 

17.4

Name: Date: 

17.4 Transformers 

A transformer is a device used to change voltage and current. You may have 

noticed the gray electrical boxes often located between two houses or 

buildings. These boxes protect the transformers that “step down” high voltage 

from power lines (13,800 volts) to standard household voltage (120 volts). 

17.4 How a transformer works: 

1. The primary coil is connected to outside power lines. Current in 

the primary coil creates a magnetic field through the secondary 

coil. 

2. The current in the primary coil changes frequently because it is 

alternating current. 

3. As the current changes, so does the strength and direction of the 

magnetic field through the secondary coil. 

4. The changing magnetic field through the secondary coil induces 

current in the secondary coil. The secondary coil is connected to 

the wiring in your home. 

Transformers work because the primary and secondary coils have different numbers of turns. If the secondary 

coil has fewer turns, the induced voltage in the secondary coil is lower than the voltage applied to the primary 

coil. You can use the proportion below to figure out how number of turns affects voltage: 

17.4

Page 2 of 2 

A transformer steps down the power line voltage (13,800 volts) to standard household voltage 

(120 volts). If the primary coil has 5,750 turns, how many turns must the secondary coil have? 

Solution: 

V N 

= 

V N 

1 1 

2 2 

13,800 volts 5750 turns 

= 

120 volts N 

1. In England, standard household voltage is 240 volts. If you brought your own 

hair dryer on a trip there, you would need a transformer to step down the voltage 

before you plug in the appliance. If the transformer steps down voltage from 240 

to 120 volts, and the primary coil has 50 turns, how many turns does the 

secondary coil have? 

2. You are planning a trip to Singapore. Your travel agent gives you the proper 

transformer to step down the voltage so you can use your electric appliances 

there. Curious, you open the case and find that the primary coil has 46 turns and 

the secondary has 24 turns. Assuming the output voltage is 120 volts, what is the 

standard household voltage in Singapore? 

N 

3. A businessman from Zimbabwe buys a transformer so that he can use his own electric appliances on a trip to 

the United States. The input coil has 60 turns while the output coil has 110 turns. Assuming the input voltage 

is 120 volts, what is the output voltage necessary for his appliances to work properly? (This is the standard 

household output voltage in Zimbabwe.) 

4. A family from Finland, where standard household voltage is 220 volts, is planning a trip to Japan. The 

transformer they need to use their appliances in Japan has an input coil with 250 turns and an output coil 

with 550 turns. What is the standard household voltage in Japan? 

2 

5. An engineer in India (standard household voltage = 220 volts) is designing a transformer for use on her 

upcoming trip to Canada (standard household voltage = 120 volts). If her input coil has 240 turns, how many 

turns should her output coil have? 

6. While in Canada, the engineer buys a new electric toothbrush. When she returns home she designs another 

transformer so she can use the toothbrush in India. This transformer also has an input coil with 240 turns. 

How many turns should the output coil have? 

2 

= 50 turns 

17.4

Name: Date: 

17.4 Electrical Power 

How do you calculate electrical power? 

In this skill sheet you will review the relationship between electrical power and Ohm’s law. As you work through 

the problems, you will practice calculating the power used by common appliances in your home. 

During everyday life we hear the word watt mentioned in reference to things like light bulbs and electric bills. 

The watt is the unit that describes the rate at which energy is used by an electrical device. Energy is never created 

or destroyed, so “used” means it is converted from electrical energy into another form such as light or heat. Since 

energy is measured in joules, power is measured in joules per second. One joule per second is equal to one watt. 

To calculate the electrical power “used” by an electrical component, multiply the voltage by the current. 

A kilowatt (kWh) is 1,000 watts or 1,000 joules of energy per second. On an electric bill you may have noticed 

the term kilowatt-hour. A kilowatt-hour means that one kilowatt of power has been used for one hour. To 

determine the kilowatt-hours of electricity used, multiply the number of kilowatts by the time in hours. 

. 

• You use a 1,500-watt heater for 3 hours. How many kilowatt-hours of electricity did you use? 

You used 4.5 kilowatt-hours of electricity. 

1. Your oven has a power rating of 5,000 watts. 

Current × Voltage = Power, or P = IV 

1 kilowatt 

1,500 watts × = 1.5 kilowatts 

1,000 watts 

1.5 kilowatts × 3 hours = 

4.5 kilowatt-hours 

a. How many kilowatts is this? 

b. If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh) are used? 

c. If your town charges $0.15 per kWh, what is the cost to use the oven to bake the cookies? 

2. You use a 1,200-watt hair dryer for 10 minutes each day. 

a. How many minutes do you use the hair dryer in a month? (Assume there are 30 days in the month.) 

b. How many hours do you use the hair dryer in a month? 

c. What is the power of the hair dryer in kilowatts? 

d. How many kilowatt-hours of electricity does the hair dryer use in a month? 

e. If your town charges $0.15 per kWh, what is the cost to use the hair dryer for a month? 

3. Calculate the power rating of a home appliance (in kilowatts) that uses 8 amps of current when plugged into 

a 120-volt outlet. 

17.4

Page 2 of 2 

4. Calculate the power of a motor that draws a current of 2 amps when connected to a 12 volt battery. 

5. Your alarm clock is connected to a 120 volt circuit and draws 0.5 amps of current. 

a. Calculate the power of the alarm clock in watts. 

b. Convert the power to kilowatts. 

c. Calculate the number of kilowatt-hours of electricity used by the alarm clock if it is left on for one year. 

d. Calculate the cost of using the alarm clock for one year if your town charges $0.15 per kilowatt-hour. 

6. Using the formula for power, calculate the amount of current through a 75-watt light bulb that is connected 

to a 120-volt circuit in your home. 

7. The following questions refer to the diagram. 

a. What is the total voltage of the circuit? 


c. What is the power of the light bulb? 

8. A toaster is plugged into a 120-volt household circuit. It draws 5 amps of 

current. 

a. What is the resistance of the toaster? 

b. What is the power of the toaster in watts? 

c. What is the power in kilowatts? 

9. A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit. 

a. What is the current through the dryer? 

b. What is the resistance of the dryer? 

c. How many kilowatt-hours of electricity are used by the dryer if it is used for 4 hours in one week? 

d. How much does it cost to run the dryer for one year if it is used for 4 hours each week at a cost of $0.15 

per kilowatt-hour? 

10. A circuit contains a 12-volt battery and two 3-ohm bulbs in series. 

a. Calculate the total resistance of the circuit. 

b. Calculate the current in the circuit. 

c. Calculate the power of each bulb. 

d. Calculate the power supplied by the battery. 

11. A circuit contains a 12-volt battery and two 3-ohm bulbs in parallel. 

a. What is the voltage across each branch? 

b. Calculate the current in each branch. 

c. Calculate the power of each bulb. 

d. Calculate the total current in the circuit. 

e. Calculate the power supplied by the battery. 

17.4

Page 1 of 2 

18.1 Andrew Ellicott Douglass 

Douglass, a successful American astronomer, is better known as the father of dendrochronology. 

His accomplishments in tree ring analysis and cross-dating allowed him to create a tree calendar 

dating back to AD 700 for the American Southwest. 

Vermont Native 

Andrew Ellicott Douglas 

was born on July 5, 1867 in 

Windsor, Vermont. Andrew 

was one of five children 

born to Sarah and Malcolm 

Douglass. Malcolm, an 

Episcopalian minister, and 

his wife moved frequently. 

They settled for a period of 

time in Windsor where 

Malcolm became a minister 

for St. Pauls Church and 

they raised their children. 

Douglass attended Trinity College in Hartford, 

Connecticut. An astronomer, Douglass worked at 

Harvard College Observatory from 1889-1894. While 

working for the observatory, he traveled to Peru to 

find a suitable location for another observatory. He 

helped to establish the Harvard Southern Hemisphere 

Observatory in Arequipa, Peru. 

From sunspots to tree rings 

When Douglass returned home, he met astronomer 

Percival Lowell of Boston, Massachusetts. Working for 

Lowell, Douglass set out again to find a location for an 

observatory, but this time in Arizona. In 1894, he found 

a site on a Flagstaff mesa and oversaw the building of 

the Lowell Observatory. While at the observatory, 

Douglass was Lowell’s chief assistant and worked with 

Lowell to observe the planet Mars. However, Douglass 

and Lowell did not always agree on how to use the 

gathered data and Lowell fired Douglass. 

Douglass remained in Flagstaff to teach Spanish and 

geography at what is now known as Northern Arizona 

University. While in Flagstaff, he became interested in 

tree rings and their possible connection to sunspot 

cycles. While researching the eleven-year sunspot 

cycle, he examined ponderosa pine tree rings. He 

noted that rings held information about weather 

patterns and hoped he could find a link between 

periods of drought and sunspot activity. 

18.1 

In 1906, Douglass moved to Tucson, Arizona and 

taught at the University of Arizona. Here, he created 

the science of dendrochronology. He found that 

differences in tree ring width corresponded to weather 

patterns. A period of drought produced narrower rings 

than a time of increased rainfall. In 1929, Douglass 

was able to place a date on Native American ruins in 

Arizona with accuracy. He studied Ponderosa pine tree 

rings dating back to the time of these Native American 

dwellings. He matched wooden beam samples against 

pine tree rings to determine a precise date for the 

ancient ruins. Douglass development of this crossdating 

technique was a tremendous breakthrough in 

the field of archaeology. Archaeologists now had a 

tool to date ancient ruins. 

Despite his work in tree ring analysis, Douglass 

remained an active astronomer. From 1918 to 1937, 

Douglass worked at the Steward Observatory at the 

University of Arizona. Within this period of time, he 

also wrote Climate Cycles and Tree Growth, Volumes 

I, II, and III. In 1937, he retired as director of the 

observatory and devoted his time to tree ring research. 

Dendrochronology and beyond 

Douglass quickly discovered that tree ring studies 

required time and physical space. He asked the 

University of Arizona president for a tree ring 

research facility. In 1938, Douglass became the first 

directory of the Laboratory of Tree-Ring Research at 

the University of Arizona. The Laboratory of Tree- 

Ring Research has the largest number of tree ring 

samples in the world. He remained director of the 

laboratory until 1958. 

In 1984, an asteroid was identified and named Minor 

Planet or Asteroid (2196) Ellicott, after Douglass 

middle name. Douglass died on March 20, 1962 at age 

94. Later, Spacewatch astronomer Tom Gehrels 

discovered an asteroid in 1998 using a telescope that 

Douglass had dedicated to the Steward Observatory 

many years earlier. A second asteroid was then named 

after Douglass. On the planet Mars, a crater has also 

been named in honor of Douglass.

Page 2 of 2 


1. How did Douglass move from studying planets and stars to studying trees? 

2. What is the name of the science and specific technique that Douglass discovered? 

3. How has Douglass work with tree rings been useful to archaeologists? 

4. Research: The first asteroid named after Douglass is called Minor Planet (2196) Ellicott. What is the name 

of the second asteroid named after Douglass? 

5. Research: The Harvard Southern Hemisphere Observatory, also called the Boyden Observatory, was 

originally located in Arequipa, Peru. It has moved. Where is the observatory now located? 

6. Research: Tom Gehrels is an astronomer associated with the Spacewatch program. What is the Spacewatch 

program? 

18.1

Name: Date: 

18.2 Relative Dating 

f 

Earth is very old and many of its features were formed before people came along to study them. For that reason, 

studying Earth now is like detective work—using clues to uncover fascinating stories. The work of geologists 

and paleontologists is very much like the work of forensic scientists at a crime scene. In all three fields, the 

ability to put events in their proper order is the key to unraveling the hidden story. 

Relative dating is a method used to determine the general age of a rock, rock formation, or fossil. When you use 

relative dating, you are not trying to determine the exact age of something. Instead, you use clues to sequence 

events that occurred first, then second, and so on. A number of concepts are used to identify the clues that 

indicate the order of events that made a rock formation. 

Sequencing events after a thunderstorm 

Carefully examine this illustration. It contains evidence of the following events: 

• The baking heat of the sun caused cracks to formed in the dried mud puddle. 

• A thunderstorm began. 

• The mud puddle dried. 

• A child ran through the mud puddle. 

• Hailstones fell during the thunderstorm. 

1. From the clues in the illustration, sequence the events listed above in the order in which they happened. 

2. Write a brief story that explains the appearance of the dried mud puddle and includes all the events. In your 

story, justify the order of the events. 

18.2

Page 2 of 4 

Determining the relative ages of rock formations 

Relative dating is an earth science term that describes the set of principles and techniques used to 

sequence geologic events and determine the relative age of rock formations. Below are graphics that 

illustrate some of these basic principles used by geologists. You will find that these concepts are easy to 

understand. 

Match each principle to its explanation. One relative dating term will be new to you! Which is it? There is one 

explanation that does not have a matching picture. Write the name of this explanation. 

Explanations 

3. In undisturbed rock layers, the oldest layer is at the bottom and the youngest layer is at the top. 

4. In some rock formations, layers or parts of layers may be missing. This is often due to erosion. Erosion by 

water or wind removes sediment from exposed surfaces. Erosion often leaves a new flat surface with some 

of the original material missing. 

5. Sediments are originally deposited in horizontal layers. 

6. Any feature that cuts across rock layers is younger than the layers. 

7. Sedimentary layers or lava flows extend sideways in all directions until they thin out or reach a barrier. 

8. Any part of a previous rock layer, like a piece of stone, is older than the layer containing it. 

9. Fossils can be used to identify the relative ages of the layers of a rock formation. 

18.2

Page 3 of 4 

Sequencing events in a geologic cross-section 

18.2 

Understanding how a land formation with its many layers of soil was created begins with the same 

time-ordering process you used earlier in this skill sheet. Geologists use logical thinking and geology principles 

to determine the order of events for a geologic formation. Cross-sections of Earth, like the one shown below, are 

our best records of what has happened in the past. 

Rock bodies in this cross-section are labeled A through H. One of these rock bodies is an intrusion. Intrusions 

occur when molten rock called magma penetrates into layers from below. The magma is always younger than the 

layers that it penetrates. Likewise, a fault is always younger than the layers that have faulted. A fault is a crack or 

break that occurs across rock layers, and the term faulting is used to describe the occurrence of a fault. The 

broken layers may move so that one side of the fault is higher than the other. Faulted layers may also tilt. 

10. List the rock bodies illustrated below in order based on when they formed. 

11. Relative to the other rock bodies, when did the fault occur? 

12. Compared with the formation of the rock bodies, when did the stream form? Justify your answer.

Page 4 of 4 

Extension—Creating clues for a story 

Collect some materials to use to create a set of clues that will tell a story. Examples of materials: 

construction paper, colored markers, tape, glue, scissors, different colors of modeling clay, different 

colors of sand or soil, rocks, an empty shoe box or a clear tank for clues. 

Then, give another group in your class the opportunity to sequence the clues into a story. Follow these guidelines 

in setting up your story: 

• Set up a situation that includes clues that represent at least five events. 

• Each of the five events must happen independently. In other words, two events cannot have happened at the 

same time. 

• Use at least one geology principle that you learned through this skill sheet. 

• Answer the questions below. 

13. Describe your set of clues in a paragraph. Include enough details in your paragraph so that someone can recreate 

the set of clues. 

14. What relative dating principles are represented with your set of clues? Explain how these principles are 

represented. 

15. Now, have a group of your classmates put your set of clues in order. When they are done, evaluate their 

work. Write a short paragraph that explains how they did and whether or not they figured out the correct 

sequence of clues. Describe the clue they missed if they made an error. 

18.2

Page 1 of 2 

18.2 Nicolas Steno 

18.2 

Nicolas Steno was a keen observer of nature at a time when many scientists were content to learn 

about the world by reading books. Through dissection, Steno made important advances in the field of medicine. 

Later he applied his observational skills to the field of geology, identifying three important principles that 

geologists still use to determine the order in which geological events occurred. 

Steno’s childhood 

Nicolas Steno was born in 

1638 in Copenhagen, 

Denmark. He became ill at age 

three and spent most of his 

time indoors until age six. He 

saw few children, but spent 

time listening to adults discuss 

religion. Religion later 

became an important part of 

his life. 

Steno, the son of a goldsmith, 

had skillful hands like his father. However, his skill 

was not in making jewelry. He was an expert in 

dissecting animals to learn about anatomy. He was 

fascinated by the structure of living things. 

The young scientist 

When Nicolas was not yet ten years old, his father 

died. He spent his teen years living in Copenhagen 

with a half-sister and her husband. Steno was smart, 

curious, and a good listener. He gained the attention of 

two scholars in Copenhagen. 

The first scholar, Ole Borch, welcomed Steno into his 

alchemy laboratory. There, Steno watched as 

sediments settled out of liquid solutions. He thought it 

was interesting that even when the bottom of the jar 

was bumpy, the sediments formed a smooth horizontal 

layer on top of the bumpy surface. 

Thomas Bartholin, a famous anatomist from the 

University of Copenhagen, also mentored Steno. 

Perhaps through this friendship, Steno developed a 

keen interest in dissection and anatomy. In 1660, he 

left Denmark to study medicine at the University of 

Leiden in the Netherlands. There, through careful 

dissection of mammals, he made discoveries related to 

glands, ducts, the heart, brain, and muscles. 

A shark’s tooth unlocks a mystery 

In 1665, Steno moved to Italy. The following year, 

fishermen there captured a great white shark. The 

Italian Duke Ferdinand sent the head to Steno for 

dissection. Steno carefully observed the shark’s teeth. 

They looked like glossopetrae or “tongue stones,” 

common stony items found inside rocks. 

While we now know that these tongue stones are 

fossilized remains of living things, in Steno’s time 

many people believed tongue stones either grew inside 

rocks, fell from the sky, or even fell from the Moon. 

Steno suggested a different explanation for the tongue 

stones. He said they had once been actual shark teeth! 

Then Steno started to think about how a solid object, 

like a shark tooth, could get inside another solid 

object, like a rock. 

Three important principles 

Based on his work, Steno came up with three 

important principles of geology. 

• The principle of superposition says that layers of 

sediment settle on top of each other. The oldest layers 

are on the bottom and the more recent layers are on 

top. 

• The principle of original horizontality says that 

sedimentary rock layers form in horizontal patterns, 

even if they form on a bumpy surface. 

• The principle of lateral continuity says that sediment 

layers spread out until they reach something that stops 

the spreading. 

Steno explained that the shark teeth had been in soft 

sediment that eventually hardened into a layer of rock. 

Steno used his principles to write a book about the 

geology of a region of Italy called Tuscany. Even 

today, geologists use Steno’s principles to determine 

the order in which geologic events occurred. 

Father Steno 

In 1675, Steno gave up science to become a priest. He 

died in 1686 at the age of 48. In 1988, Pope John Paul 

II beatified Steno, the first step in the process of 

naming someone a saint. Today, the Steno Museum in 

Denmark and craters on both Mars and the Moon bear 

his name.

Page 2 of 2 


1. Name and briefly describe the three important principles of geology developed by Steno. 

2. How did most people in the 1600s explain the origin of fossils? 

3. How did Steno explain the existence of tongue stones or shark teeth in rocks? 

4. How did Steno’s medical background and skills help him with his geological discoveries? 

5. Observing is very important in science. What things do you like to observe? What have you learned through 

observation? 

6. Research: Steno’s father was a goldsmith and one of his teachers was interested in alchemy. What does a 

goldsmith do? What is alchemy? How could these two fields have been helpful to Steno’s work? 

18.2

Name: Date: 

18.3 The Rock Cycle 

In Section 18.3 of your student text, you will learn about the rock cycle. Place the three main groups of rocks in 

the ovals below. Then, fill in the blank lines with the materials or processes at work in each stage of the rock 

cycle. Use this diagram as a study aid. Describe to a friend or family member what is happening at each stage. 

18.3

Name: Date: 

19.1 Earth’s Interior 

19.1

Page 1 of 2 

19.1 Charles Richter 

19.1 

Richter is the most recognized name in seismology due to the earthquake magnitude scale he 

codeveloped. But Earth science was never a subject of interest to this bright young physicist, until a mentor 

made an interesting suggestion and a “happy accident” introduced him to seismology. 

The unexpected path 

Charles F. Richter was born 

on April 26, 1900 in 

Hamilton, Ohio. When he 

was 16, Charles and his 

mother left their Ohio farm 

and moved to Los Angeles. 

Richter attended the 

University of Southern 

California from 1916–1917, 

and then earned a bachelor’s 

degree in physics at Stanford 

University. 

It was during his Ph.D. studies in theoretical physics 

at the California Institute of Technology (Caltech) that 

Richter began his work in seismology, quite by 

accident. 

In 1927, Richter was working on his Ph.D. under the 

Nobel Prize winning physicist Dr. Robert Millikan. 

One day, Dr. Millikan called Richter into his office 

and presented him with an opportunity. The Caltech 

Seismology Laboratory was in need of a physicist, and 

although Richter had never done any Earth science 

work, Dr. Millikan thought he might be a good person 

for the job. 

Richter was a little surprised, but decided to talk to 

Harry Wood, the lead scientist in charge of the lab. 

Richter became intrigued and decided to join the 

seismology lab located in Pasadena, California. 

Richter described this introduction to the science that 

would become his life’s work as a “happy accident.” 

Doing something ordinary 

One of Charles Richter’s most famous sayings is 

based on looking back at his own life: “Don’t wait for 

extraordinary circumstance to do good; try to use 

ordinary situations.” 

When he first started at the seismology lab, Richter 

was busy with the routine work of measuring 

seismograms and locating earthquakes, so that a 

catalog of epicenters and occurrence times could be 

set up. At the time, this kind of earthquake study was 

new. Harry Wood was leading the effort to use 

southern California’s active seismic setting to gain a 

better understanding of earthquakes. 

This creative setting allowed Richter to attempt to 

develop new ways to “rate” earthquakes based on the 

seismic waves they produced. Since the lab used seven 

seismographs to record activity, Richter suggested that 

they compare quakes to one another using the amplitude 

of each quake measured at all seven locations. To do this, 

the seismic readings needed to be corrected to take into 

account the differences in distance from the epicenters. 

Richter had learned of a method to do this based on large 

earthquakes, but the magnitudes that Richter was 

studying ranged from tiny to very large. 

Collaboration and success 

Richter thought that the size difference in the 

magnitudes was unmanageably large. Fellow scientist 

Dr. Beno Gutenberg suggested that they plot the 

magnitudes using powers of 10. A magnitude two 

earthquake would represent 10 times the amplitude of 

ground motion of a magnitude one. A magnitude three 

would be 100 times a magnitude one, a four would 

be 1,000 times a magnitude one, and so on. 

Richter realized this was the obvious answer to his 

problem. When he used this method and graphed the 

results, it worked! At first it could be used only for 

southern California, because the system was only 

meant to compare quakes of that region using the 

seven seismographs in their lab. 

A new way to rate earthquakes 

In 1935, Richter and Gutenberg published their 

magnitude scale system. By 1936, they had worked 

out how their system could be used in all parts of the 

world, with any type of instrument. Before this, the 

Mercalli scale had been used to rate the magnitude of 

earthquakes, but it was based on local damage to 

buildings and people’s reactions to a quake. 

Richter and Gutenberg’s scale allowed for a more 

absolute and scientific method to be used by anyone, 

anywhere in the world.

Page 2 of 2 


1. Look up the definition of each boldface word in the article. Write down the definitions and be sure 

to credit your source. 

2. What do you think you would feel like if a world reknown scientist like Dr. Robert Millikan recommended 

you for a job? How would you feel if accepting that job meant that you could no longer work closely with 

Dr. Millikan? 

3. How did Richter respond to his new job? 

4. Who helped Richter refine his idea into a working model? 

5. Name a scale other than the Richter scale that scientists use to evaluate earthquakes. 

6. Research: Why do scientists use different scales to rate earthquakes? 

7. Research: What is the difference between a seismograph and a seismometer? 

19.1

Page 1 of 2 

19.1 Jules Verne 

19.1 

Jules Verne was an enormously successful nineteenth century author. He introduced the world to 

science fiction. His stories of adventure and imaginative methods of travel were decades ahead of their time. His 

ideas have entertained and inspired generations of readers. Several of his books have been made into popular 

movies. 

A great imagination yearning for adventure 

Jules Verne was born on 

February 8, 1828 in the 

busy port city of Nantes, 

France. The oldest of five 

children, Jules came from a 

family with a strong 

seafaring tradition rich with 

the spirit for travel and 

adventure. 

The family’s summer home 

just outside the city of 

Nantes may have inspired Jules to search for adventure. 

The house was on the banks of the Loire River. Jules and 

his younger brother Paul would often play outside and 

watch ships from all over the world sail down the river. 

The boys would make up stories about these ships; 

where they were from, where they were going, the 

characters aboard the vessels, and especially the wild 

escapades they had during their journeys. 

While Jules’ father was part of a family that included 

many travelers, he did not intend his sons to follow in 

those footsteps. Both Jules and Paul were sent to a 

boarding school, right in their hometown of Nantes. 

There they were expected to get an education that 

would take them out of the seafaring class and into 

wealthy society. 

Expectations and creativity clash 

After graduating from the boarding school, Verne’s 

father sent him to Paris in 1847, where he was 

expected to study law. While he studied and prepared 

for the bar exam, Verne found his time was 

increasingly spent writing. 

An uncle that had been asked to check up on Verne 

saw that he was having some quiet success writing 

the words for operas. This uncle understood Verne’s 

true calling. He began to introduce Verne to people 

involved with Paris’ literary circles. 

Verne managed to get a few plays published and even 

performed. Although busy, he still was able to get his 

law degree. This came in handy, because as soon as 

Verne’s father found out about his writing, he 

furiously stopped sending his son money. With his 

money supply gone, Verne took a job as a stockbroker. 

He hated this job, yet was quite good at it. 

A career takes off 

Around this time Verne began to meet important 

authors like Alexander Dumas and Victor Hugo. They 

offered advice to the young writer. In 1857 Verne 

married, and was encouraged by his wife to pursue his 

dream of writing. 

Verne became a fan of Edgar Allen Poe, modelling 

some of his early work on Poe’s style, and in 1897 he 

wrote a sequel to one of Poe’s unfinished novels. In 

1862 Verne met Pierre-Jules Hetzel, an editor with a 

keen eye and feel for what a story needed to be 

successful. 

Verne’s writing had often been criticized for being too 

scientific. Hetzel knew how to make Verne’s stories 

appeal to the common person. In 1863, Verne began 

publishing his “Extraordinary Voyages” series of 

novels and thankfully quit his stockbroking job. 

In rapid succession Verne tackled the sky, the sea, the 

land, and even space in his novels. In 1863 he wrote 

Five Weeks in a Balloon, a story about exploring 

Africa in a hot air balloon. In 1864 he wrote Journey 

to the Center of the Earth, a trek by scientists down a 

volcano on their way to Earth’s core. In 1865 he wrote 

From Earth to the Moon, a visionary work that 

preceded NASA missions by 100 years. He published 

20,000 Leagues Under the Sea in 1869, introducing 

the world to Captain Nemo, a mysterious genius who 

built the futuristic submarine The Nautilus. 

Jules Verne’s 65 novels took readers on marvelous 

adventures, introducing futuristic ideas that while not 

always based on scientific facts, incorporated concepts 

that inspired future thinkers and entertained millions. 

Verne died in 1905, as the world’s most translated 

author, making up for his lack of scientific training 

and actual travel experience with a vivid imagination.

Page 2 of 2 


1. Why do you think Jules Verne’s novels appealed so widely to readers around the world? 

2. Research which novels written by Verne have been made into movies. Have any of them won awards? 

3. Research the bar exam. Why would Jules Verne need to pass it? 

4. Research Victor Hugo and explain why meeting him may have been important to Verne. 

5. Research some of the machines, ideas, and predictions Verne made in his novels that have come to exist 

today. 

19.1

Page 1 of 2 

19.2 Alfred Wegener 

19.2 

Alfred Wegener was a man ahead of his time. He was an astronomer and a meteorologist, yet his 

greatest work was in the field of earth science. His theory of plate tectonics is widely accepted today. Yet, in 

1912 when he proposed the idea, he was ridiculed. It took fifty years for other scientists to find the evidence that 

would prove his theory. 

The young man 

Alfred Wegener was born 

in Berlin in 1880. He was 

the son of a German 

minister who ran an 

orphanage. As a boy, he 

became interested in 

Greenland, and as a 

scientist, he went to 

Greenland several times to 

study the movement of air 

masses over the ice cap. 

This was at a time when 

most scientists doubted the existence of the jet stream. 

Just after his fiftieth birthday, he died there in a 

blizzard during one of his expeditions. 

Wegener graduated from the University of Berlin in 

1905 with a degree in astronomy. Soon, however, his 

interest shifted to meteorology. This was a new and 

exciting field of science. Wegener was one of the first 

scientists to track air masses using weather balloons. 

No doubt, he got the idea from his hobby of flying in 

hot air balloons. In 1906, he and his brother set a 

world record by staying up in a balloon for over fiftytwo 

hours. 

The search for evidence 

In 1910, in a letter to his future bride, Wegener wrote 

about the way that South America and Africa seemed 

to fit together like pieces of a puzzle. To Wegener, this 

was not just an odd coincidence. It was a mystery that 

he felt he must solve. He began to look for evidence to 

prove that the continents had once been joined 

together and had moved apart. 

Fossils of a small reptile had been found on the west 

coast of Africa and the east coast of South America. 

That meant that this reptile had lived in both places at 

the same time millions of years ago. Wegener figured 

that the only way this was possible was if the two 

continents were connected when animals were alive. 

They could not have traveled across the ocean. 

Geological evidence 

There was also geological evidence. The rock 

structures and types of rocks on the coasts of these two 

continents were identical. Again, Wegener could find 

no explanation for how this could have happened by 

accident on opposite sides of the ocean. The rock 

structures had to have been formed at the same time 

and place under the same conditions. 

A study of climates produced other evidence. Coal 

deposits had been found in Antarctica and in England. 

Since coal is formed only from plants that grow in 

warm, wet climates, Wegener concluded that those 

land masses must have once been near the equator, far 

from their locations today. 

Ridiculed and rejected 

Wegener explained that all of the continents had been 

part of one large land mass about 300 million years 

ago. This super-continent was called Pangaea, a Greek 

word that means “all earth.” It broke up over time, and 

the pieces have been drifting apart ever since. 

Wegener compared the drifting continents to icebergs. 

Wegener’s peers called his theory “utter rot!” Many 

scientists attacked him with rage and hostility. 

Wegener had two main problems. First, he was an 

unknown outsider, not a geologist, who was 

challenging everything that scientists believed at the 

time. Second, he was not able to explain what caused 

the continents to drift. While there seemed to be 

evidence to show that they had indeed moved, he 

could not identify a force that made it happen. 

About fifty years after Wegener proposed his theory, a 

scientist named Harry Hess made a discovery about 

sea floor spreading that seemed to support Wegener’s 

ideas. As a result, the theory of plate tectonics was 

finally accepted by most scientists.

Page 2 of 2 


1. Explain the significance of Greenland in Wegener’s life. 

2. What world record did Wegener set in 1906? 

3. Why could Wegener be called an interdisciplinary scientist? Identify the fields of science of which he was 

knowledgeable. 

4. Explain how the fossil of a small reptile provided evidence to help prove Wegener’s theory of drifting 

continents. 

5. How did the discovery of coal deposits in England and Antarctica strengthen Wegener’s argument? 

6. Research: In his search for evidence to support his theory of drifting continents, Wegener studied the rock 

strata in the Karroo section of South Africa and the Santa Catarina section of Brazil. He also studied the 

Appalachian Mountains in North America and the Scottish Highlands. Use a library or the Internet to 

research these areas. What evidence do they provide for Wegener’s theory? Share your findings with the 

class. 

7. What were the two main problems that Wegener faced when he tried to convince others that his theory of 

drifting continents was valid? 

8. Research: Wegener and some colleagues drew maps of what they thought the world looked like at different 

times as the super continent broke up and the continents drifted apart. Use a library or the Internet to find 

pictures of these maps. Make a poster displaying Wegener’s vision of the world at: 

• 300 million years ago (Pangaea) 

• 225 million years ago (Permian period) 

• 200 million years ago (Triassic period) 

• 135 million years ago (Jurassic period) 

• 65 million years ago (Cretaceous period) 

• Today 

19.2

Page 1 of 2 

19.2 Harry Hess 

19.2 

Harry Hammond Hess was a geology professor at Princeton University and served many years in the 

U.S. Navy. In 1962, Hess published a landmark paper that described his theory of sea floor spreading. Hess 

also made major contributions to our national space program. 

A globe-trotting geologist 

Harry Hammond Hess was 

born in New York City on 

May 24, 1906. He first 

studied electrical 

engineering at Yale 

University, but later 

changed his major to 

geology. He received his 

degree in 1927. 

After graduation, Hess 

worked for two years as a 

mineral prospector in southern Rhodesia (currently 

Zimbabwe, Africa). He then returned to the United 

States to study at Princeton University. In 1932, Hess 

became a professor of geology at Princeton. Years 

later, his geological research took him to the far depths 

of the Pacific Ocean floor. 

The Navy commander 

Harry Hess was part of the Naval Reserve. In 1941 he 

was called to active duty. His first duty during World 

War II was in New York City where he tracked enemy 

positions in the North Atlantic. He later commanded 

an attack transport ship in the Pacific. 

Although he was a Naval commander, Hess seized the 

opportunity of being on a ship to further his geological 

research. Between battles, Hess and his crew gathered 

data about the structure of the ocean floor using the 

ship’s sounding equipment. They recorded thousands 

of miles worth of depth recordings. 

In 1945, Hess measured the deepest point of the ocean 

ever recorded—nearly 7 miles deep. He also 

discovered hundreds of flat-topped mountains lining 

the Pacific Ocean floor. He named these unusual 

mountains “guyouts” (after his first geology professor 

at Princeton). 

A ground breaking theory 

After the war, Hess continued to study guyouts, 

midocean ridges, and minerals. In 1959, his research 

led him to propose the ground breaking theory of sea 

floor spreading. At first, Hess’ idea was met with 

some resistance because little information was 

available to test this concept. 

In 1962, his sea floor spreading theory was published 

in a paper titled “History of Ocean Basins.” Hess 

explained that sea floor spreading occurs when molten 

rock (or magma) oozes up from inside the Earth along 

the mid-oceanic ridges. This magma creates new sea 

floor that spreads away from the ridge and eventually 

sinks into the deep oceanic trenches where it is 

destroyed. Hess’ theory became one of the most 

important contributions to the study of plate tectonics. 

The sea floor spreading theory explained many 

unsolved geological questions. Most geologists at the 

time believed that the oceans had existed for at least 4 

billion years. But they wondered why there wasn’t 

more sediment deposited on the ocean floor after such 

a long time period. 

Hess explained that the ocean floor is continually 

being recycled and that sediment has been 

accumulating for no more than 300 million years. This 

is about the time period needed for the ocean floor to 

spread from the ridge crest to the trenches. Hess’s 

theory helped geologists understand why the oldest 

fossils found on the sea floor are 180 million years old 

at most, while marine fossils found on land may be 

much older. 

From the ocean to the moon 

Harry Hess also played a key role in developing our 

country’s space program. In 1962, President John F. 

Kennedy appointed Hess as Chairman of the Space 

Science Board—a NASA advisory group. During the 

late 1960s, Hess helped plan the first landing of 

humans on the moon. He was part of a committee 

assigned to analyze rock samples brought back by the 

Apollo 11 crew. 

Harry Hess died in August 1969, only one month after 

the successful Apollo 11 lunar mission. He was buried 

in the Arlington National Cemetery. After his death, 

he was awarded NASA’s Distinguished Public Service 

Award.

Page 2 of 2 


1. How did Harry Hess’ career in the Navy contribute to his geological research? 

2. What were some of the geological discoveries Hess made while aboard his attack transport ship? 

3. Describe Hess’ theory of sea floor spreading. 

4. How did Hess’ sea floor spreading theory explain why so little sediment is deposited on the ocean floor? 

5. What were Hess’ contributions to space research? 

6. Research: Harry Hess made significant contributions in the fields of geology, geophysics, and mineralogy. 

What scientific society established the Harry H. Hess Medal and what achievements does it recognize? 

19.2

Page 1 of 2 

19.2 John Tuzo Wilson 

19.2 

John Tuzo Wilson was a professor at the University of Toronto whose love for adventure helped him 

make major contributions in the field of geophysics. His research on plate tectonics explained volcanic island 

formation and led to the discovery of transform faults. He also described the formation of oceans, a process later 

named the Wilson Cycle. 

A noteworthy family 

John Tuzo Wilson was born 

in Ottawa, Canada on 

October 24, 1908. His 

adventurous parents helped 

to expand Canada’s frontiers. 

Wilson’s mother, Henrietta 

Tuzo, was a famous 

mountaineer. Mount Tuzo in 

western Canada was named 

in her honor after she scaled 

its peak. Wilson’s father, also 

named John, helped plan the 

Canadian Arctic Expedition of 1913 to 1918. He also 

helped develop airfields throughout Canada. 

In 1930, Wilson was the first graduate of geophysics 

from the University of Toronto. He earned a second 

degree from Cambridge University. In 1936, Wilson 

received a doctorate in geology from Princeton 

University. 

An adventurous scholar 

Throughout his career, Wilson enjoyed traveling to 

unusual locations. While a student at Princeton, 

Wilson became the first person to scale Mount Hague 

in Montana—an elevation of 12,328 feet. 

When World War II broke, Wilson served in the Royal 

Canadian Army. After the war, Wilson led an 

expedition called Exercise Musk-Ox. He directed ten 

army vehicles 3,400 miles through the Canadian 

Arctic. This journey proved that people could travel to 

Canada’s north country. 

In 1946, Wilson began his 30-year career as a 

professor of geophysics at the University of Toronto. 

While a professor, Wilson mapped glaciers in 

Northern Canada. Between 1946 and 1947, he became 

the second Canadian to fly over the North Pole during 

his search for unknown Arctic islands. 

Plate tectonics and a hot idea 

Many scientists contributed to the development of the 

plate tectonics theory. However, they had difficulty 

explaining the formation of volcanic islands. These 

islands, like the Hawaiian Islands, are thousands of 

kilometers away from plate boundaries. 

In the early 1960s, Wilson solved the volcanic island 

mystery. He explained that sometimes a single hot 

mantle plume will break through a plate and form a 

volcanic island. As the plate moves over the mantle 

plume, a chain of islands forms. At first this theory was 

rejected. Finally, in 1963, Wilson published his paper. 

Slipping and sliding plates 

In 1965, Wilson proposed that a type of plate 

boundary must connect ocean ridges and trenches. He 

suggested that a plate boundary ends abruptly and 

transforms into major faults that slip horizontally. 

Wilson called these boundaries “transform faults.” 

Wilson’s idea was confirmed and quickly became a 

major milestone in the plate tectonics theory. The San 

Andreas Fault of southern California is a well-known 

transform fault. 

Opening and closing ocean basins 

Wilson was one of the first geologists to link seafloor 

spreading with land geology. In 1967, Wilson 

published an article that described the repeated 

process of ocean basins opening and closing. This 

process later became known as the Wilson Cycle. 

Geologists believe that the Atlantic Ocean basin 

closed millions of years ago. This event led to the 

formation of the Appalachian and Caledonian 

mountain systems. The basin later re-opened to form 

today’s Atlantic Ocean. 

An honored geologist 

Wilson’s contributions to the field of geophysics led 

to many honors and awards throughout his career. In 

1967, Wilson became the principle of Erindale 

College at the University of Toronto. From 1974 to 

1985, Wilson served as director of the worldrenowned 

Ontario Science Center. On April 15, 1993, 

Wilson died at age 84.

Page 2 of 2 


1. How did John Tuzo Wilson’s parents contribute to his passion for the outdoors? 

2. Why is Wilson sometimes referred to as an adventurous scholar? 

3. Describe Wilson’s theory of how volcanic islands are formed. 

4. What did Wilson discover about plate boundaries and the formation of faults? 

5. What is the Wilson Cycle? Give an example of this process. 

6. Research: On which continent are mountains named in honor of John Tuzo Wilson? 

19.2

Name: Date: 

19.3 Earth’s Largest Plates 

19.3

Name: Date: 

19.4 Continental United States Geology 

You have learned about the plates that make up the surface of Earth. You have also learned how plates are formed 

at mid-ocean ridges and are destroyed at subduction zones. Here is a very brief look at how plate tectonics 

formed the land mass that we call the United States. It covers only the last chapter of the Earth history of the 48 

contiguous states. 

The full history of the surface of Earth is a very long and complicated story. To give you an idea of the difficulty 

of understanding the full story, imagine this: A young child is given a new box of modeling clay. In the box are 

four sticks of differently colored clay. The child plays with the clay for hours making different figures. First a set 

of animals, then a fort, and so on. Between each idea, the child balls up all of the clay. Now imagine that it’s the 

next day and the ball of swirled clay colors is in your hand. Your task is to figure out what the child made and in 

what order. 

That sounds impossible, and it probably is. The amazing thing is that geologists have figured out a lot of the 

equally difficult story of Earth’s surface. We have a pretty good idea about how the early crust was formed. And 

we know that there was a super continent called Rodinia that formed before Pangaea, the last super continent. 

But like the child’s clay figures, the further back we look, the more the clues are mixed up. 

The last chapter 

Our story begins late. Most of the history of Earth has already passed. During this time rift valleys formed that 

split continents into smaller pieces. First the land moved apart on both sides of a rift valley. Then, once the rift 

valley opened wide enough, water flooded in and a new ocean was born. Underwater, the rift valley then became 

a mid-ocean ridge. 

At the same time, subducting plates acted like conveyor belts. Anything that was part of a subducting plate was 

carried toward the subduction zone. In this way continents were carried together. Collisions between continents 

welded them together. Mountain ranges formed at the point of contact. 

The combination of rifting and subduction worked together to form, destroy, and reform the early continents. You 

can see that the result is very much like playing with modeling clay. 

The craton 

Even though most of Earth’s history had passed, 

it was still an incredibly long time ago. Rifting 

had broken up Rodinia, but subduction had not 

yet formed Pangaea. The break-up of Rodinia 

left six continents scattered across the world 

oceans. These continents were not the continents 

that we see today. One of these, Gondwanaland, 

was larger than the others put together. 

19.4

Page 2 of 4 

Two other continents are important to our story. They are called Baltica and Laurentia. At the center of 

Laurentia was a core piece that was very old even then. This core piece is called the craton. The craton 

had been changed again and again, but it was stable inside Laurentia. Today the craton of Laurentia 

forms the central United States. 

You may wonder where these names came from. After all, these continents were gone many millions of years 

before humans appeared on Earth. They are modern names proposed and adopted by geologists. 

The first collision 

Rifting and subduction caused Baltica to move 

in a jerky path. Eventually, Baltica collided with 

Laurentia to form a larger combined continent. 

This new continent is called Laurasia. A high 

mountain range formed where the colliding 

continents made contact. This mountain range 

lay deep inside Laurasia. Today the remains of 

this high mountain range form our northern 

Appalachian Mountains. 

Gondwanaland collides 

Subduction continued to bring continents 

together. Next mighty Gondwanaland was drawn 

ever closer to Laurasia. Gondwanaland collided 

just below where Laurentia and Baltica collided 

with each other. This new collision raised 

another set of mountains that continued the 

northern Appalachians into what are now the 

southern Appalachians. The combined 

Appalachians were as high as the Himalayans of 

today! The super continent Pangaea was then 

complete and the lofty Appalachian Mountains 

stood near its center. 

Pangaea breaks up 

Pangaea did not remain together for very long, only a few tens of millions of years. The same rifting process that 

broke up Rodinia split the new super continent into smaller pieces. Our future East Coast had been deep inside 

the central part of Pangaea. But in the break-up, a rift valley split our eastern shore away from what is now 

Africa. Instead of an inland place, our East Coast became an eastern shore. 

The East Coast after Pangaea 

One of the amazing things in geology is how quickly mountain ranges are eroded away. After Pangaea broke up, 

the Appalachians completely eroded away. All that was left was a flat plain! The sediments produced from this 

erosion formed deep layers on the eastern shore and near-shore waters. These coastal margin sediments make up 

most of the eastern states today. But wait a minute; today we see rounded mountains where there had been only 

flat plains. What formed the rounded Appalachian Mountains of today? 

19.4

Page 3 of 4 

When a mountain is formed, some of it is pressed deep into the mantle by the weight of the mountain 

above. It’s like stacking wood blocks in water. As the stack grows taller, it also sinks deeper. Erosion 19.4 

takes a tall mountain down quickly. With the top gone, its bottom rebounds back to the surface. In this 

way, the Appalachian Mountains that we see today are actually the rebounded lower section of the mountains that 

once had been pressed deep below Earth’s surface. 

The West Coast and the Ancestral Rocky Mountains 

There are two Rocky Mountain ranges. The first is called the Ancestral Rocky Mountains. The Ancestral Rocky 

Mountains were formed when subduction caused an ancient collision with Laurentia. The collision struck 

Laurentia on the side that would become our western states. In other words, the Ancestral Rocky Mountains 

already existed before Pangaea formed. The Ancestral Rockies were then heavily weathered and the sediment 

deposited on the surrounding plains. Today the Front Range of Colorado is part of the exposed remains of the 

Ancestral Rocky Mountains. 

Pangaea and the West Coast 

Our West Coast did not exist as Pangaea began to break up. The shoreline was near the present eastern border of 

California. What would become our West Coast states were sediments and islands scattered in the ocean to the 

west. 

North America began to move westward as it 

was rifted apart from Pangaea. A subduction 

zone appeared in front of the moving continent. 

As the ocean floor dove under the westwardmoving 

continent, these sediments, islands and 

even pieces of ocean floor became permanently 

attached to the continent. Our western shore 

grew in this way, forming the shape that we see 

today. 

The modern Rocky Mountains 

The mid-ocean ridge that was forming the subducting ocean plate was not too far away to the west. As the plate 

subducted, the mid-ocean ridge got closer and closer to the edge of the continent. This changed the way that the 

plate subducted. The result was that stronger push pressure caused the continent to buckle well back from its 

edge. In this way, the modern Rocky Mountains were formed near the remains of the Ancestral Rocky 

Mountains.

Page 4 of 4 

Inland volcanoes 

The subducting plate also caused volcanoes to form and erupt 

inland. These eruptions produced the Sierra Nevada 

Mountains to the south and High Cascades to the north. 

A small plate disappears 

The plate that had been subducting along the southern West Coast was 

small. Eventually it disappeared when its mid-ocean ridge was 

subducted. This changed the western edge of the United States from a 

converging boundary to a transform boundary. Now instead of one 

plate diving under another, the remaining Pacific Plate slides by the 

West Coast. Today this slide-by motion is well known as the San 

Andreas Fault. 

When subduction stopped along the lower West Coast, the Sierra 

volcanoes became extinct. Magma cooled and solidified below the 

surface. Today this cooled magma is exposed as the domes of Yosemite 

National Park. Further north, the Pacific Plate is still subducting under 

the West Coast. That subduction continues to drive the volcanoes of the 

High Cascades. 

The United States today 

In geologic terms, the East Coast is quiet and the West Coast is active. The contiguous United States are part of 

the North American Plate. The active eastern boundary of the plate lies in the middle of the Atlantic Ocean, far 

from our East Coast. But the active western boundary is also our western shore. The San Andreas Fault slowly 

moves slivers of California northward. Baja California will eventually be attached to San Diego. Map makers 

won’t have to redraw New England, but they will have to watch for West Coast changes. The good news is that 

they’ll have plenty of time to make those changes. 

19.4

Name: Date: 

20.1 Averaging 

The most common type of average is called the mean. To find the mean, just add all the data, then divide the total 

by the number of items in the data set. This type of average is used daily by many people; teachers and students 

use it to average grades, meteorologists use it to average normal high and low temperatures for a certain date, and 

sports statisticians use it to calculate batting averages, among many other things. 

Seven students in Mrs. Ramos’ homeroom have part time jobs on the weekends. Some of them baby sit, some 

mow lawns, and others help their parents with their businesses. They all listed their hourly wages to see how their 

own pay compares to that of the others. Here is the list: $11.00, $4.50, $12.20, $5.25, $8.77, $15.33, $5.75. What 

is the average (mean) hourly wage earned by students in Mrs. Ramos’ homeroom? 

1. Find the sum of the data: $11.00 + $4.50 + $12.20 + $5.25 + $8.77 + $15.33 + $5.75 = $62.80 

2. Divide the sum ($62.80) by the number of items in the data set (7): $62.80 ÷ 7 ≈ $8.97 

3. Solution: The average hourly wage of the students in Mrs. Ramos’ homeroom is $8.97. 

1. Jill’s test grades in science class so far this grading period are: 77%, 64%, 88%, and 82%. What is her 

average test grade so far? 

2. The total team salaries in 2005 for teams in a professional baseball league are as follows: Team One, 

$63,015,833 (24 players); Team Two, $48,107,500 (24 players); Team Three, $81,029,500 (29 players); 

Team Four, $62,888,192 (22 players); Team Five, $89,487,426 (18 players). What is the average amount of 

money spent by a team in this league on players salaries in 2005? 

3. During a weekend landscaping job, Raul worked 8 hours, Ben worked 15 hours, Michelle worked 22 hours, 

Rosa worked 5 hours, and Sammie worked 15 hours. What was the average number of hours worked by one 

person during this landscaping job? If each worker was paid $12.00 an hour, what was the average pay per 

person for the job? 

4. The 8th grade girls basketball team at George Washington Carver Middle School played the team from 

Rockwood Valley Middle School last night. The Rockwood Valley team won, 53-37. Altogether, there were 

three girls who scored 11 points each, four who scored 8 points each, one who scored 6 points, two who 

scored 4 points each, four who scored 2 points each, three who scored one point each, and two girls who did 

not score at all. What is the average number of points scored by a player on either team? 

5. During a weekend car trip that covered 220 miles each way, Rowan kept track of the price per gallon of 

regular unleaded gasoline at different gas stations along the way. Here is the list he kept: $2.79, $3.23, $3.99, 

$2.89, $3.09, $2.99, $2.97, $3.11, $2.88, $3.01, $3.00, $2.99. What was the average price per gallon of gas 

among the different gas stations on the list? 

20.1

Name: Date: 

20.1 Finding an Earthquake Epicenter 

The location of an earthquake’s epicenter can be determined if you 

have data from at least three seismographic stations. One method of 

finding the epicenter utilizes a graph and you need to know the 

difference between the arrival times of the P- and S-waves at each of 

three seismic stations. Another method uses a formula and you need to 

know the arrival times and speeds of the P- and S-waves. The only 

other items you need to find an epicenter are a calculator, a compass, 

and a map. 

Finding the epicenter using a graph 

Table 1 provides the arrival time difference between P- and S-waves. Use this value to find the distance to the 

epicenter on the graph. Record the distance values in the table in the third column from the left. 

1 

2 

3 

Station 

name 

Table 1: Seismic wave arrival time and distance to the epicenter 

Arrival time difference 

between P- and S-waves 

15 seconds 

25 seconds 

42 seconds 

Distance to epicenter 

in kilometers 

Scale distance to 

epicenter in 

centimeters 

20.1

Page 2 of 5 

Locating the epicenter on a map 

Once you have determined the distance to the epicenter for three stations in kilometers, you can use a 

map to locate the epicenter. The steps are as follows: 

Step 1: Determine the radius of a circle around each seismographic station on a map. The radius will be 

proportional to distance from the epicenter. Use the formula below to convert the distances in kilometers to 

distances in centimeters. For this situation, we will assume that 100 kilometers = 1 centimeter. Record the scale 

distances in centimeters in the fourth column of Table 1. 

----------------- 

1 cm 

100 km 

Step 2: Draw circles around each seismic station. Use a geometric compass to make circles around each station. 

Remember that the radius of each circle is proportional to the distance to the epicenter. 

Step 3: The location where the three circles intersect is the location of the epicenter. 

= 

--------------------------------------------------------------x 

distance to epicenter in km 

20.1

Page 3 of 5 

Finding the epicenter using a formula 

To calculate the distance to the epicenter for each station, you will use the equation: 

Table 2 lists the variables that are used in the equation for finding the distance to the epicenter. This table also 

lists values that are given to you. 

Table 2: Variables for the equation to calculate the distance to the epicenter 

Variable What it means Given 

d p distance traveled by P-waves r p = 5 km/s 

r p 

t p 

d s 

r s 

t s 

speed of P-waves 

travel time of P-waves 

distance traveled by S-waves 

speed of S-waves 

travel time of S-waves 

Distance = Rate × Time 

For each of the practice problems, assume that the speed of the P-waves will be 5 km/s and the speed of the Swaves 

will be 3 km/s. Also, because the P- and S-waves come from the same location, we can assume the 

distance traveled by both waves is the same. 

distance traveled by P-waves = distance traveled by S-waves 

d p 

= 

Since the travel time for the S-waves is longer, we can say that, 

d s 

rp × tp = rs × ts travel time of S-waves = ( travel time of P-waves) 

+ ( extra time) 

ts = tp + ( extra time) 

rp × tp = 

rs × ( tp + extra time) 

r s = 3 km/s 

d p = d s 

20.1

Page 4 of 5 

20.1 

For each of the practice problems, assume that the speed of the P-waves is 5 kilometers per second, and 

the speed of the S-waves is 3 kilometers per second. The first problem is done for you. Show your work for all 

problems. 

1. S-waves arrive to seismographic station A 85 seconds after the P-waves arrive. What is the travel time for 

the P-waves? 

2. S-waves arrive to another seismographic station B 80 seconds after the P-waves. What is the travel time for 

the P-waves to this station? 

3. A third seismographic station C records that the S-waves arrive 120 seconds after the P-waves. What is the 

travel time for the P-waves to this station? 

4. From the calculations in questions 1, 2, and 3, you know the travel times for P-waves to three seismographic 

stations (A, B, and C). Now, calculate the distance from the epicenter to each of the stations using the speed 

and travel time of the P-waves. Use the equation: distance = speed × time. 

5. Challenge question: You know that the travel time for P-waves to a seismographic station is 200 seconds. 

a. What is the difference between the arrival times of the P- and S-waves? 

b. What is the travel time for the S-waves to this station? 

6. Table 3 includes data for three seismographic stations. Using this information, perform the calculations that 

will help you fill in the rest of the table, except for the scale distance row. 

Table 3: Calculating the distance to the epicenter 

Variables Station 1 Station 2 Station 3 

Speed of P-waves rp 5 km/s 5 km/s 5 km/s 

Speed of S-waves rs 3 km/s 3 km/s 3 km/s 

Time between the arrival of P- 

and S-waves 

ts - tp 70 seconds 115 seconds 92 seconds 

Total travel time of P-waves t p 

Total travel time of S-waves ts Distance to epicenter in 

kilometers 

Scale distance to epicenter in 

centimeters 

5 km 

× t p 

s 

3 km 

= × (tp + 85 s) 

s 

⎛ 5 km ⎞ 

⎜ ⎟tp ⎝ s ⎠ 

⎛ 3 km ⎞ 

= ⎜ ⎟tp 

+ 255 km) 

⎝ s ⎠ 

⎛ 2 km ⎞ 

⎜ ⎟tp 

⎝ s ⎠ 

= 255 km 

t = 

128 s 

d p , d s 

p

Page 5 of 5 

Once you have determined the distance to the epicenter for three stations in kilometers, you can use a 

map to locate the epicenter. The steps are as follows: 

Step 1: Determine the radius of a circle around each seismographic station on a map. The radius will be 

proportional to distance from the epicenter. Use the formula below to convert the distances in kilometers to 

distances in centimeters. For this situation, we will assume that 200 kilometers = 1 centimeter. Record the scale 

distances in centimeters in the last row of Table 3. 

----------------- 

1 cm 

200 km 

Step 2: Draw circles around each seismic station. Use a geometric compass to make circles around each station. 

Remember that the radius of each circle is proportional to the distance to the epicenter. 

Step 3: The location where the three circles intersect is the location of the epicenter. 

= 

--------------------------------------------------------------x 

distance to epicenter in km 

20.1

Name: Date: 

20.2 Volcano Parts 

20.2

Name: Date: 

20.3 Basalt and Granite 

As you read Section 20.3 of your student text, you will learn how basalt and granite form. You’ll learn about 

ways they are alike and ways that they are different. The Venn diagram below can help you organize this 

information. As you learn about these types of rock, place facts that apply to both in the space where the circles 

intersect. Place facts that apply to only one type of rock in its individual space. Use this diagram as a study aid. 

20.3

Name: Date: 

21.2 Calculating Concentration of Solutions 

What’s the difference between regular and extra-strength cough syrup? Is the rubbing alcohol in your parents’ 

medicine cabinet 70% isopropyl alcohol, or is it 90% isopropyl alcohol? The differences in these and many other 

pharmaceuticals is dependent upon the concentration of the solution. Chemists, pharmacists, and consumers 

often find it necessary to distinguish between different concentrations of solutions. Concentration is commonly 

expressed as of solute per mass of solution, known as mass percent. 

Mass of solute 

Mass percent = 100 

Total mass of solution × 

Remember that a solution is defined as a mixture of two or more substances that is homogenous at the molecular 

level. The solvent is the substance that is present in the greatest amount. All other substances in the solution are 

known as solutes. 

• What is the mass percent concentration of a solution made up of 12 grams of sugar and 300. grams of water? 

Solution: 

In this case, the solute is sugar (12 g), and the total mass of the solution is the mass of the sugar plus the 

mass of the water, (12 g + 300. g). 

Substituting into the formula, where c = the percent concentration, we have: 

12 g 12 g 

c = × 100 = × 100 = 3.8% 

12 g + 300 g 312 g 

The concentration of a solution of 12 grams of sugar and 300. grams of water is 3.8%. 

• How many grams of salt and water are needed to make 150 grams of a solution with a concentration of 

15% salt? 

Solution: 

Here, we are given the concentration (15%) and the total mass of the solution (150 g). We are trying to find 

the mass of the solute (salt). Substituting into the same formula, where m is the mass of the salt, we have: 

m m 

15% = × 100, so 0.15 = , and 0.15 × (150 g) = m = 22.5 g 

150 g 150 g 

Since the total mass of the solution is 150 grams, and we now know that 22.5 grams are salt, that leaves: 

150 grams solution - 22.5 grams salt = 127.5 grams of water 

To make 150 grams of a solution with a concentration of 15% salt, you would need 22.5 grams of salt 

and 127.5 grams of water. 

21.2

Page 2 of 2 

Find the mass percent concentration of each solution or mixture. 

1. 5 grams of salt in 75 grams of water 

2. 40 grams of cinnamon in 2,000 grams of flour 

3. 1.5 grams of chocolate milk mix in 250 grams of 1% milk 

Find the mass of the solute in each situation. 

4. 1,000 grams of a 40% salt water solution 

5. 30 grams of a 12.5% sugar water solution 

6. 555 grams of a 25% sand and soil “solution” 

Carefully read and answer each of the following questions. 

7. Dawn is mixing 450 grams of dishwashing liquid with 600 grams of water to make a solution for her little 

brother to blow bubbles. What is the concentration of the dishwashing liquid? 

8. How many grams of glucose are needed to prepare 250 grams of a 5% glucose and water solution? 

9. Jill mixes 4 grams of vanilla extract into the 800 grams of cake batter she has prepared. What is the 

concentration of vanilla in her “solution” of cake batter? 

10. Challenge: Find the amount of red food coloring (in grams) necessary to add to 50 grams of water to prepare 

a 15% solution of red food coloring in water. 

21.2

Name: Date: 

21.2 Solubility 

In this skill sheet you will practice solving problems about solubility. You will use solubility values to identify 

solutions that are saturated, unsaturated, or supersaturated. Finally, you will practice your skills in interpreting 

temperature-solubility graphs. 

What is solubility? 

A solution is defined as a mixture of two or more substances that is homogenous at the molecular level. The 

substance present in the greatest amount is called the solvent. The other substances are known as solutes.The 

degree to which a solute dissolved is described by its solubility value. This value is the mass in grams of the 

solute that can dissolve in a given volume of solvent under certain conditions. 

For example, the solubility of table salt (NaCl) is 1 gram per 2.7 milliliters of water at 25 °C. Another way to 

state this solubility value is to say that 0.37 grams of salt will dissolve in one milliliter of water at 25 °C. Do you 

see that these values mean the same thing? 

1 gram NaCL 0.37 gram NaCL 

= 

2.7 ml H 0 i 25 ° C 2.7 ml H 0 i 

25 ° C 

2 2 

Information about the solubility of table salt and other substances is presented in the table below. Use these 

values to complete the questions that follow. 

Substance Solubility Value (grams/100 mL water 25°C) 

Table salt (NaCl) 37 

Sugar (C 12H 22O 11) 200 

Baking soda (NaHCO 3) 10 

Chalk (CaCO 3) insoluble 

Talc (Mg silicates) insoluble 

1. Chalk and talc are listed as “insoluble” in the table. What do you think this term means? In your response, 

come up with a reason to explain why chalk and talc cannot dissolve in water. 

2. Come up with a reason to explain why table salt, sugar, and baking soda dissolve in different amount for the 

same set of conditions (same volume and temperature). 

3. How much table salt would dissolve in 540 mL of water if the water was 25 °C? 

4. What volume of water would you need to dissolve 72 grams of salt at 25 °C? 

5. What volume of water at 25 °C would you need to dissolve 50 grams of sugar? 

6. How much baking soda will dissolve in 10 milliliters of water at 25 °C? 

21.2

Page 2 of 3 

Saturated, unsaturated, and supersaturated solutions 

The solubility value for a substance indicates how much solute is present in a saturated solution. When the 

amount of solute is less than the solubility value for a certain volume of water, we say the solution is unsaturated. 

When the amount of solute is more than the solubility value for a certain volume of water, we say the solution is 

supersaturated. 

Use the table on the previous page to help you fill in the table below. In each situation, is the solution saturated, 

unsaturated, or supersaturated? 

Substance Amount of substance in 

200 mL of water at 25°C 

Table salt (NaCl) 37 grams 

Sugar (C 12H 22O 11) 500 grams 

Baking soda (NaHCO 3) 20 grams 

Table salt (NaCl) 100 grams 

Sugar (C 12H 22O 11) 210 grams 

Baking soda (NaHCO 3) 25 grams 

Saturated, unsaturated, or 

supersaturated? 

21.2

Page 3 of 3 

The influence of temperature on solubility 

Have you noticed that sugar dissolves much easier in hot tea than in iced tea? The solubility of some substances 

increases greatly as the temperature of the solvent increases. For other substances, the dissolving rate changes 

very little. A solubility graph (sometimes called a solubility curve) can be used to show how temperature affects 

solubility. 

Below is a table of some imaginary substances dissolved in water at different temperatures. Study the table and 

then answer the questions. 

Substance dissolved in 

100 mL of water 

Solubility values (grams per 100 mL of water) 

at different temperatures 

10 °C 30 °C 50 °C 70 °C 90 °C 

gas A 0.2 0.2 0.1 0.08 0.05 

gas B 0.1 0.05 0.02 0.01 0.005 

solid A 30 32 40 55 74 

solid B 40 43 39 41 45 

1. Use graph paper to make two solubility graphs of the data in the table. On one graph, plot the data for gases 

A and B. On the other graph, plot the data for solids A and B. Use two different colors to plot the data for A 

and for B. Label the x-axis, “Temperature (°C).” Label the y-axis, “Solubility value (grams/100 mL H 2O).” 

2. How does the solubility of gases A and B differ from the solubility of solids A and B in water? Explain your 

response. 

3. For which substance does temperature seem to have the greatest influence on solubility? 

4. For which substance does temperature seem to have the least influence? 

5. If you had 500 mL of water at 70°C and you made a saturated solution by adding 205 grams of a substance, 

which of the substances above would you be adding? 

6. Organisms that live in ponds and lakes depend on dissolved oxygen to survive. Explain how the amount of 

dissolved oxygen in a pond or lake might vary with the seasons (winter, spring, summer, and fall). Justify 

your ideas. 

21.2

Name: Date: 

21.2 Salinity and Concentration Problems 

Bodies of water like ponds, lakes, and oceans contain solutions of dissolved substances. Often these substances 

are in small quantities, measured in parts per thousand (ppt), parts per million (ppm), and parts per billion (ppb). 

This skill sheet will provide you with practice in using these quantities and in doing calculations with them. 

Unit conversions 

Table 1 below provides unit conversions that will be helpful to you as you complete this skill sheet. 

Review: working with small concentrations 

When working with small concentrations, remember that the units of the numerator and denominator must 

match, as shown in the examples below. 

A. Parts per thousand (ppt) 

Example: 0.009 grams of phosphate in about 1000 grams of oxygenated water makes a solution that has an 

phosphate concentration of 0.009 ppt. 

B. Parts per million (ppm) 

Example: A good level of oxygen in a pond is 9 ppm. This means that there are 9 milligrams of oxygen for every 

one liter (1000 grams) of oxygenated water. 

C. Parts per billion (ppb) 

Table 1: Unit Conversions 

Milligrams = Grams = Kilograms = Liters of water 

1 0.001 0.000 001 0.000 001 

10 0.01 0.000 01 0.000 01 

1,000 1 0.001 0.001 

1,000,000 1,000 1 1 

1,000,000,000 1,000,000 1,000 1,000 

9 

----------------------------milligrams 

1 liter 

0.009 grams 

---------------------------- = 0.009 ppt 

1,000 grams 

= 

9 

----------------------------milligrams 

= -------------------------------------------------- 

9 milligrams 

= 9 ppm 

1,000 grams 1,000,000 milligrams 

Example: The concentration of trace elements in seawater is very low. For example, the concentration of iron in 

seawater is 0.06 ppb. This means that there are 0.06 mg of iron in 1,000 liters of water. One thousand liters is 

equal to 1,000 times 1,000 grams of seawater. 

0.06 

------------------------------------milligrams 

1,000 liters 

------------------------------------------------ 

0.06 milligrams 0.06 milligrams 0.06 milligrams 

= = --------------------------------------- = 

------------------------------------------------------------- = 0.06 ppb 

1,000 × 1,000 grams 1,000,000 grams 1,000,000,000 milligrams 

21.2

Page 2 of 3 

Work through these example problems and check your answers. Then you will be ready to try the practice 

problems on your own. 

• There are 16 grams of salt in 984 grams of water. What is the salinity of this solution? 

Solution: 

• A liter of solution has a salinity of 40 ppt. How many grams of salt are in the solution? How many grams of 

pure water are in the solution? 

Solution: 

• You measure the salinity of a seawater sample to be 34 ppt. How many grams of salt are in this sample if the 

mass is 2 kilograms? 

Solution: First, remember that there are 1,000 grams per kilogram. If a solution is given in parts per 

thousand, you can think of it as “grams per 1,000 grams” or “grams per kilogram.” Therefore, you can set up 

a proportion like this: 

Next, solve for x. 

16 grams salt 16 grams salt 

salinity = = = 16 ppt 

984 grams water + 16 grams salt 1,000 grams solution 

40 grams salt 40 grams salt 

40 ppt = = 

1,000 grams solution 40 grams salt + x grams water 

1,000 grams solution = 40 grams salt + x grams water 

1,000 grams solution - 40 grams salt = 960 grams water 

34 grams salt x grams salt 

= 

1 kilogram solution 2 kilograms solution 

34 grams salt × 

2 kilograms solution 

x = 

1 kilogram solution 

x = 68 grams salt 

21.2

Page 3 of 3 

For each problem, show your work. 

1. Complete Table 2 below: 

Place Salinity 

(ppt) 

Salton Sea 

44 

California 

Great Salt Lake 280 

Utah 

Mono Lake 210 

California 

Pacific Ocean 87 

Table 2: Salinity of Famous Places 

Amount of salt in 1 liter 

(grams) 

2. How many grams of salt are in 2 liters of seawater that has a salinity of 36 ppt? 

Amount of pure water in 1 liter 

(grams) 

3. A one-liter sample of seawater contains 10 grams of salt. What is the salinity of this sample? 

4. You want to make a salty solution that has the same salinity as the Dead Sea. The salinity of the Dead Sea is 

210 ppt. Write a recipe for how you would make 2 liters of this solution. 

5. Five kilograms of seawater contains 30 grams of salt. What is the salinity of the volume of seawater? 

6. You measure the salinity of a seawater sample to be 30 ppt. How many grams of salt are in this sample if the 

mass is 1.5 kilograms? 

7. A solution has 2 grams of a substance in 1,000,000 grams of solution. Would you describe the concentration 

of the substance in solution as 2 parts per million or parts per billion? 

8. A solution has 5 grams of a substance in 1,000,000,000 grams of solution. Would you describe the 

concentration of the substance as 5 ppb or 5 ppm? 

9. Menthol is a substance that tastes sweet and minty and causes a cooling effect on your tongue. The taste 

threshold for menthol is 400 ppb. Could you taste menthol if there were 400 milligrams in 1,000,000 grams 

of menthol solution? Could you taste menthol if there were 400 milligrams in 1000 liters of menthol 

solution? 

10. Above-ground pipelines are used to transport natural gas, an important energy source. Gas leaks are 

potential problems with the pipelines. German Shepherd dogs can be trained to detect the gas leaks. The 

dogs sniff along the pipeline and then indicate a leak by perking up their ears or pawing the ground. The 

most sensitive electronic devices can detect gas leaks as low as 50 ppm. A German Shepherd can detect a 

gas leak as low as 1 ppb. How many times more sensitive is the dog as compared to the electronic device? 

21.2

Name: Date: 

21.3 Calculating pH 

The pH of a solution is a measure of the concentration of hydrogen ions (H+) in the solution. The pH scale, 

which ranges from 0 to 14, provides a tool to assess the degree to which a solution is acidic or basic. As you may 

remember, solutions with low pH values are very acidic and contain high concentrations of hydrogen ions. Why 

does a low pH value mean a high concentration of H+? The answer has to do with what pH means 

mathematically. In this skill sheet, we will examine how pH values are calculated. 

How do you calculate pH? 

The pH value for any solution is equal to the negative logarithm of the hydrogen ion (H+) concentration in that 

solution. The formula is written this way: 

pH – log H + 

= [ ] 

Concentration of hydrogen ions is implied by placing brackets (“[ ]”) around H+. 

A term used by scientists to describe the concentration of a substance in a solution is molarity. Molarity (M) 

means how many moles of a substance are present in a given volume of solution. 

For hydrogen ions in solutions, the concentration generally ranges from 10 to 10 –14 M. The larger the molarity, 

the greater the concentration of H+ in the solution. If a solution had a H + concentration of 10 –3 M, the 

corresponding pH value would be: 

pH – log 10 3 – 

= [ ] 

10 pH 

10 3 – 

– [ ] 

For a solution with an H + concentration of 10 –5 M, the corresponding pH value would be: 

pH 

= 

= 

pH = 3 

– [ – 3] 

pH – log 10 5 – 

= [ ] 

10 pH 

pH 

= 

= 

pH = 

5 

10 5 – 

– [ ] 

– [ – 5] 

The first solution has a higher H + concentration than the second solution (10 –3 M versus 10 –5 M); however, its 

pH value is a smaller number. Strong acids have small pH values. Larger pH values (like 14) have lower 

concentrations of H + , and the solutions represent weaker acids. 

21.3

Page 2 of 2 

1. Practice working with numbers that have exponents. In the blank provided, write greater than, less 

than, or equals. 

a. 10 –2 ____________________ 10 –3 

b. 10 –14 ____________________ 101 c. 10 –7 ____________________ 0.0000001 

d. 10 0 ____________________ 101 2. Solutions that range in pH from 0 to 7 are acidic. Solutions that range in pH from 7 to 14 are basic. Solutions 

that have pH of 7 are neutral. The hydrogen ion concentrations for some solutions are given below. Use the 

pH formula to determine which is an acid, which is a base, and which is neutral. 

a. Solution A: The hydrogen ion concentration is equal to 10 -1 M. 

b. Solution B: The hydrogen ion concentration is equal to 0.0000001 M. 

c. Solution C: The hydrogen ion concentration is equal to 10 –13M. 3. Orange juice has a hydrogen ion concentration of approximately 10 –4 M. What is the pH of orange juice? 

4. Black coffee has a hydrogen ion concentration of roughly 10 –5 M. Is black coffee a stronger or weaker acid 

than orange juice? Justify your answer and provide all relevant calculations for supporting evidence. 

5. Pure water has a hydrogen ion concentration of 10 –7 M. What is the pH of water? Would you say water is an 

acid or a base? Explain your answer. 

6. A solution has a pH of 11. What is the H + concentration of the solution? Is this solution an acid or a base? 

7. A solution has a pH of 8.4. What is the H + concentration of this solution? 

8. Acids are very good at removing hard water deposits from bathtubs, sinks, and glassware. Your father goes 

to the store to buy a cleaner to remove such deposits from your bathtub. He has a choice between a product 

containing lemon juice (H + =10 –2.5 M) and one containing vinegar (H + =10 –3.3 M). Which product would 

you recommend he purchase? Explain your answer. 

21.3

Name: Date: 

22.1 Groundwater and Wells Project 

When it rains, some of the water that falls on Earth seeps into the ground, while some water flows over the 

surface into local streams or lakes. Some water is absorbed by plants and some evaporates back into the 

atmosphere. The water that seeps into the ground flows downward, moving through empty spaces between soil, 

sand, or rocks. It continues its journey until it reaches rock through which it cannot easily move. Then, it starts to 

fill the spaces between the rock and soil above. The top of this wedge of water is called the water table. 

The water that fills the empty spaces is called groundwater. Areas that groundwater easily moves through are 

called aquifers. Aquitards are bodies of rock where water can move through—but very slowly. If the aquitard 

does not allow any water to pass, it is called an aquiclude. Groundwater comes from precipitation (rain and snow 

melt), from lakes or rivers that leak water, and even from extra water not used by agricultural crops when they are 

irrigated. 

Groundwater is a very important source of drinking water. According to the US Geological Survey, 51% of 

Americans get their drinking water from groundwater. 99% of the rural population in the US uses groundwater 

for drinking. 37% of agricultural water, which is mostly used for irrigation comes from groundwater. 

Groundwater is obtained by digging wells. The water fills the well underground and a pump inside pumps it up to 

the surface where it travels through pipes to bring it to our homes and businesses. 

This project will help you learn more about groundwater movement and wells. 

Materials: 

• GeoBox • ½”to ¾” white 

stone; rounded is 

better 

(approximately 

1,800 mL total) 

• Plastic wrap • Food dye - dark 

colors 

• Wooden skewer or 

dowel with diameter 

less than ½” 

• 3 wells (½” inside 

diameter PVC pipe 

with caps; 4 well 

holes near cap 

drilled with 13/64 

drill bit) 

• ¼” plastic foam; one 

piece 7 ¾” x 13 ¾”; 

second piece 7 ¾” x 

9" 

• 8-10 cotton swabs • Tape 

• Watering can or 

beaker 

• Caulk or plumbers 

putty (something 

that can be molded 

around the PVC 

wells for 

waterproofing) 

22.1

Page 2 of 3 

Constructing the model: 

1. Line the inside of the GeoBox with plastic wrap so that it comes up and over the edges of the box. 

2. Hold well #2 in the middle of the GeoBox, with the cap end sitting directly on the bottom of the GeoBox. 

Add approximately 1,800 mL of the rock, surrounding the well. The rock should just cover the holes of the 

well and the well should stand on its own. 

3. The larger plastic foam sheet will be layered next on top of the rock. In order to put it down, carefully poke 

the well through it so it fits over the well. Now place on top of it the plastic wrap that will come up and over 

the edges. Because you need to also make a hole in the plastic wrap through which to fit the well, use the 

caulk or putty to mold around the well and onto the plastic wrap to keep it water proof. 

4. Once this is set, hold well #3 in place on the right side 

(diagram A) and add approximately 2,000 mL of stone 

down on the surface, so that it surrounds well #3 and holds 

it upright. 

5. Now add approximately 1,300 mL of stone to the left side 

of the GeoBox to create a diagonal plane of stone that runs 

highest from the left edge to level just right of well #2. 

6. Place well #1 in the built up area of stone on the left side of 

the GeoBox, just above, but not touching the first plastic 

foam layer (as well #3 is). Make sure that the stone is 

covering the holes in the well. 

7. Place the smaller plastic foam sheet over well #1 and well 

#2, again poking holes in the plastic foam so that the sheet 

can sit on the rock layers below. This sheet will be slanted 

down towards the middle. 

8. Again you will cover just the sheet with plastic wrap which will come up 

and over the edge on three sides. Caulk the two wells that poke through 

this sheet. 

9. Use the remaining 3,000 mL of stone to fill the tray up to the top so that 

what is visible is just stone and three well tops. See photo at right. 

10. Tape one cotton swab to the end of the skewer or wooden rod so that the 

cotton swab reaches out from the end of the wood. See diagram B at right. 

11. Dye the water that you will be using for precipitation a dark color, such as 

blue, red, or green. 


a. Which well/s would you expect to collect water when it rains? 

b. If contamination entered from the surface, what well would you expect to first show contaminated 

water? 

c. Will well #2 get contaminated from surface contamination? Why? 

22.1

Page 3 of 3 

Testing the model: 

1. Watch the water flow closely as you do this experiment. 

2. Sprinkle or pour the dyed water into the top layer of rock to simulate precipitation, without allowing the 

water to precipitate into the wells. The dye will make it easier to see the water as it travels. 

3. Regularly check the wells with the cotton swab/dowel rods to see if water has entered the wells. In this way, 

you can also see which well collected water the quickest. 

4. For a demonstration of the movement of surface pollution—dye water another color and allow this 

contaminated water to percolate through the layers. Use new cotton swabs attached to the wooden rods to 

visualize if and when the wells will get contaminated. The cotton swab should change color as the two dyes 

mix. 

Thinking about what you observed: 

a. Which wells collected water when it rained? Was your hypothesis correct? 

b. Which well was first to be contaminated? Was your hypothesis correct? 

c. What does the plastic wrap/plastic foam layer represent? Label diagram C appropriately. 

d. What do the rock layers represent? Label diagram C appropriately. 

e. Did well #2 get contaminated from surface contamination? Why? Was your hypothesis correct? 

f. What effect would pumping from well #1 have on movement of surface contamination? Pumping from 

well #2? 

g. What would happen if there was a dry spell and the water table and thus the groundwater was lowered to 

below well #1? Would any well be able to pump water? 

h. If well #3 were located near the coast, what effect might pumping freshwater too quickly have on the 

water in the well? 

i. When you dig a well, how might you decide how deep to dig it? 

22.1

Name: Date: 

22.2 The Water Cycle 

As you study Section 22.2 in your student text, you will learn about the processes that move water around our 

planet. Together, these processes form the water cycle. Use the word box to help you label the water cycle 

diagram below. Some words may be used more than once. 

• condensation • groundwater flow • evaporation • water vapor 

transport 

• percolation • transpiration • precipitation 

Answer the following questions. Use the diagram above and Section 22.2 of your text to help you. 

1. Name two water cycle processes that are driven by the Sun. Explain the Sun’s role in each. 

2. How is wind involved in the water cycle? 

3. How does gravity affect the water cycle? 

22.2

Name: Date: 

24.1 Period and Frequency 

The period of a pendulum is the time it takes to move through one 

cycle. As the ball on the string is pulled to one side and then let go, the 

ball moves to the side opposite the starting place and then returns to 

the start. This entire motion equals one cycle. 

Frequency is a term that refers to how many cycles can occur in one 

second. For example, the frequency of the sound wave that 

corresponds to the musical note “A” is 440 cycles per second or 440 hertz. The unit hertz (Hz) is defined as the 

number of cycles per second. 

The terms period and frequency are related by the following equation: 

1. A string vibrates at a frequency of 20 Hz. What is its period? 

2. A speaker vibrates at a frequency of 200 Hz. What is its period? 

3. A swing has a period of 10 seconds. What is its frequency? 

4. A pendulum has a period of 0.3 second. What is its frequency? 

5. You want to describe the harmonic motion of a swing. You find out that it take 2 seconds for the swing to 

complete one cycle. What is the swing’s period and frequency? 

6. An oscillator makes four vibrations in one second. What is its period and frequency? 

7. A pendulum takes 0.5 second to complete one cycle. What is the pendulum’s period and frequency? 

8. A pendulum takes 10 seconds to swing through 2 complete cycles. 

a. How long does it take to complete one cycle? 

b. What is its period? 

c. What is its frequency? 

9. An oscillator makes 360 vibrations in 3 minutes. 

a. How many vibrations does it make in one minute? 

b. How many vibrations does it make in one second? 

c. What is its period in seconds? 

d. What is its frequency in hertz? 

24.1

Name: Date: 

24.1 Harmonic Motion Graphs 

A graph can be used to show the amplitude and period of an object in harmonic motion. An example of a graph 

of a pendulum’s motion is shown below. 

The distance to which the pendulum moves away from its center point is call the amplitude. The amplitude of a 

pendulum can be measured in units of length (centimeters or meters) or in degrees. On a graph, the amplitude is 

the distance from the x-axis to the highest point of the graph. The pendulum shown above moves 20 centimeters 

to each side of its center position, so its amplitude is 20 centimeters. 

The period is the time for the pendulum to make one complete cycle. It is the time from one peak to the next on 

the graph. On the graph above, one peak occurs at 1.5 seconds, and the next peak occurs at 3.0 seconds. The 

period is 3.0 – 1.5 = 1.5 seconds. 

1. Use the graphs to answer the following questions 

a. What is the amplitude of each vibration? 

b. What is the period of each vibration? 

24.1

Page 2 of 2 

2. Use the grids below to draw the following harmonic motion graphs. Be sure to label the y-axis to 

indicate the measurement scale. 

a. A pendulum with an amplitude of 2 centimeters and a period of 1 second. 

b. A pendulum with an amplitude of 5 degrees and a period of 4 seconds. 

24.1

Name: Date: 

24.2 Waves 

A wave is a traveling oscillator that carries energy from one place to another. A high point of a wave is called a 

crest. A low point is called a trough. The amplitude of a wave is half the distance from a crest to a trough. The 

distance from one crest to the next is called the wavelength. Wavelength can also be measured from trough to 

trough or from any point on the wave to the next place where that point occurs. 

• The frequency of a wave is 40 Hz and its speed is 100 meters per second. What is the wavelength of this 

wave? 

Solution: 

1. On the graphic at right label the following 

parts of a wave: one wavelength, half of a 

wavelength, the amplitude, a crest, and a 

trough. 

a. How many wavelengths are represented 

in the wave above? 

b. What is the amplitude of the wave shown 

above? 

100 m/s 100 m/s 

= = 

2.5 meters per cycle 

40 Hz 40 cycles/s 

The wavelength is 2.5 meters. 

24.2

Page 2 of 2 

2. Use the grids below to draw the following waves. Be sure to label the y-axis to indicate the 

measurement scale. 

a. A wave with an amplitude of 

1 cm and a wavelength of 2 cm 

b. A wave with an amplitude of 

1.5 cm and a wavelength of 

3cm 

3. A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed. 

4. A wave has a speed of 50 m/s and a frequency of 10 Hz. Calculate its wavelength. 

5. A wave has a speed of 30 m/s and a wavelength of 3 meters. Calculate its frequency. 

6. A wave has a period of 2 seconds and a wavelength of 4 meters.Calculate its frequency and speed. 

Note: Recall that the frequency of a wave equals 1/period and the period of a wave equals 1/frequency. 

7. A sound wave travels at 330 m/s and has a wavelength of 2 meters. Calculate its frequency and period. 

8. The frequency of wave A is 250 hertz and the wavelength is 30 centimeters. The frequency of wave B is 

260 hertz and the wavelength is 25 centimeters. Which is the faster wave? 

9. The period of a wave is equal to the time it takes for one wavelength to pass by a fixed point. You stand on a 

pier watching water waves and see 10 wavelengths pass by in a time of 40 seconds. 

a. What is the period of the water waves? 

b. What is the frequency of the water waves? 

c. If the wavelength is 3 meters, what is the wave speed? 

24.2

Name: Date: 

24.2 Wave Interference 

Interference occurs when two or more waves are at the same location at the same time. For example, the wind 

may create tiny ripples on top of larger waves in the ocean.The superposition principle states that the total 

vibration at any point is the sum of the vibrations produced by the individual waves. 

Constructive interference is when waves combine to make a larger wave. Destructive interference is when waves 

combine to make a wave that is smaller than either of the individual waves. Noise cancelling headphones work 

by producing a sound wave that perfectly cancels the sounds in the room. 

This worksheet will allow you to find the sum of two waves with different wavelengths and amplitudes. The 

table below (and continued on the next page) lists the coordinates of points on the two waves. 

1. Use coordinates on the table and the graph paper (see last page) to graph wave 1 and wave 2 individually. 

Connect each set of points with a smooth curve that looks like a wave. Then, answer questions 2–9. 

2. What is the amplitude of wave 1? 

3. What is the amplitude of wave 2? 

4. What is the wavelength of wave 1? 

5. What is the wavelength of wave 2? 

6. How many wavelengths of wave 1 did you draw? 

7. How many wavelength of wave 2 did you draw? 

8. Use the superposition principle to find the wave that results from the interference of the two waves. 

a. To do this, simply add the heights of wave 1 and wave 2 at each point and record the values in the last 

column. The first four points are done for you. 

b. Then use the points in last column to graph the new wave. Connect the points with a smooth curve. You 

should see a pattern that combines the two original waves. 

9. Describe the wave created by adding the two original waves. 

x-axis 

(blocks) 

Height of wave 1 

(y-axis blocks) 



Height of wave 1 + wave 2 


0 0 0 0 

1 0.8 2 2.8 

2 1.5 0 1.5 

3 2.2 –2 0.2 

4 2.8 0 

24.2

Page 2 of 3 

x-axis 

(blocks) 





5 3.3 2 

6 3.7 0 

7 3.9 –2 

8 4 0 

9 3.9 2 

10 3.7 0 

11 3.3 –2 

12 2.8 0 

13 2.2 2 

14 1.5 0 

15 0.8 –2 

16 0 0 

17 –0.8 2 

18 –1.5 0 

19 –2.2 –2 

20 –2.8 0 

21 –3.3 2 

22 –3.7 0 

23 –3.9 –2 

24 –4 0 

25 –3.9 2 

26 –3.7 0 

27 –3.3 –2 

28 –2.8 0 

29 –2.2 2 

30 –1.5 0 

31 –0.8 –2 

32 0 0 

Height of wave 1 + wave 2 


24.2

Page 3 of 3 

24.2

Name: Date: 

24.3 Decibel Scale 

The loudness of sound is measured in decibels (dB). Most sounds fall between zero and 100 on the decibel scale 

making it a very convenient scale to understand and use. Each increase of 20 decibels (dB) for a sound will be 

about twice as loud to your ears. Use the following table to help you answer the questions. 

10-15 dB A quiet whisper 3 feet away 

30-40 dB Background noise in a house 

65 dB Ordinary conversation 3 feet away 

70 dB City traffic 

90 dB A jackhammer cutting up the street 10 feet away 

100 dB Listening to headphones at maximum volume 

110 dB Front row at a rock concert 

120 dB The threshold of physical pain from loudness 

• How many decibels would a sound have if its loudness was twice that of city traffic? 

Solution: 

City traffic = 70 dB 

Adding 20 dB doubles the loudness. 

70 dB + 20 dB = 90 dB 

90 dB is twice as loud as city traffic. 

1. How many times louder than a jackhammer does the front row at a rock concert sound? 

2. How many decibels would you hear in a room that sounds twice as loud as an average (35 dB) house? 

3. You have your headphones turned all the way up (100 dB). 

a. If you want them to sound half as loud, to what decibel level must the music be set? 

b. If you want them to sound 1/4 as loud, to what decibel level must the music be set? 

4. How many times louder than city traffic does the front row at a rock concert sound? 

5. When you whisper, you produce a 10-dB sound. 

a. When you speak quietly, your voice sounds twice as loud as a whisper. How many decibels is this? 

b. When you speak normally, your voice sounds 4 times as loud as a whisper. How many decibels is this? 

c. When you yell, your voice sounds 8 times as loud as a whisper. How many decibels is this? 

24.3

Name: Date: 

24.3 The Human Ear 

Write the name of the part that corresponds to each letter in the diagram. Then write the function of each 

part in the spaces on the next page. 

24.3

Page 2 of 2 

a. ______________________________________________________________________________ 

b. ______________________________________________________________________________ 

c. ______________________________________________________________________________ 

d. ______________________________________________________________________________ 

e. ______________________________________________________________________________ 

f. ______________________________________________________________________________ 

g. ______________________________________________________________________________ 

24.3

Name: Date: 

24.3 Standing Waves 

A wave that is confined in a space is called a standing wave. 

Standing waves on the vibrating strings of a guitar produce the 

sounds you hear. Standing waves are also present inside the chamber 

of a wind instrument. 

A string that contains a standing wave is an oscillator. Like any 

oscillator, it has natural frequencies. The lowest natural frequency is 

called the fundamental. Other natural frequencies are called 

harmonics. The first five harmonics of a standing wave on a string 

are shown to the right. 

There are two main parts of a standing wave. The nodes are the 

points where the string does not move at all. The antinodes are the 

places where the string moves with the greatest amplitude. 

The wavelength of a standing wave can be found by measuring the length of two of the “bumps” on the string. 

The first harmonic only contains one bump, so the wavelength is twice the length of the individual bump. 

1. Use the graphic below to answer these questions. 

a. Which harmonic is shown in each of the strings below? 

b. Label the nodes and antinodes on each of the standing waves shown below. 

c. How many wavelengths does each standing wave contain? 

d. Determine the wavelength of each standing wave. 

24.3

Page 2 of 2 

2. Two students want to use a 12-meter rope to create standing waves. They first measure the speed at 

which a single wave pulse moves from one end of the rope to another and find that it is 36 m/s. This 

information can be used to determine the frequency at which they must vibrate the rope to create 

each harmonic. Follow the steps below to calculate these frequencies. 

a. Draw the standing wave patterns for the first six harmonics. 

b. Determine the wavelength for each harmonic on the 12-meter rope. Record the values in the table 

below. 

c. Use the equation for wave speed (v = fλ) to calculate each frequency. 

Harmonic Speed (m/s) Wavelength 

(m) 

1 36 

2 36 

3 36 

4 36 

5 36 

6 36 

d. What happens to the frequency as the wavelength increases? 

e. Suppose the students cut the rope in half. The speed of the wave on the rope only depends on the 

material from which the rope is made and its tension, so it will not change. Determine the wavelength 

and frequency for each harmonic on the 6-meter rope. 

Harmonic Speed (m/s) Wavelength 

(m) 

1 36 

2 36 

3 36 

4 36 

5 36 

6 36 

f. What effect did using a shorter rope have on the wavelength and frequency? 

Frequency 

(Hz) 

Frequency 

(Hz) 

24.3

Name: Date: 

24.3 Waves and Energy 

A wave is an organized form of energy that travels. The amount of energy a wave has is proportional to its 

frequency and amplitude. Therefore, higher energy waves have a higher frequency and/or a higher amplitude. 

Remember that the frequency is measured in hertz. The frequency of 1 Hz equals one wave cycle per second. 

For each set of diagrams, identify which of the standing waves has the 

highest energy and which has the lowest energy. 

Answers for frequency and energy: 

Standing wave Frequency Energy 

A lowest lowest 

B medium medium 

C highest highest 

Answers for amplitude and energy: 

Standing wave Frequency Energy 

A lowest lowest 

B highest highest 

1. When you drop a stone into a pool, water waves spread out from where the stone landed. Why? 

2. Ian and Igor have opposite ends of a jump rope and perform the following demonstration. First they moved 

the rope up and down one time a second, then two times a second, and then three times a second. Describe 

the trend in frequency for the jump rope and the trend in energy used by Ian and Igor for this demonstration. 

3. One wave has a frequency of 30 Hz and another has a frequency of 100 Hz. Both waves have the same 

amplitude. Which wave has more energy? 

4. On a calm day ocean waves are about 0.1 meter high. However, during a hurricane, ocean waves might be as 

much as 14 meters high. If both waves have the same frequency, during which set of conditions do the waves 

have more energy? 

5. Which wave has more energy: a wave that has an amplitude of 3 centimeters and a frequency of 2 Hz or a 

wave with an amplitude of 3 meters and a frequency of 2 Hz? 

6. The loudness of sound is related to its amplitude. Which sound wave would have the least energy: a lowvolume 

wave at 1,000 Hz or a high-volume (loud) wave at 1,000 Hz? 

7. The frequency of microwaves is less than that of visible light waves. Which type of wave is likely to have 

greater energy? 

8. Standing wave C in the first graphic above represents 1.5 wavelengths. Draw a standing wave that represents 

2 wavelengths. Compare the energy and frequency of this standing wave to A, B, and C. 

24.3

Name: Date: 

24.3 Palm Pipes Project 

A palm pipe is a musical instrument made from a simple material—PVC pipe. To play a palm pipe, you hit an 

open end of the pipe on the palm of your hand, causing the air molecules in the pipe to vibrate. These vibrations 

create the sounds that you hear. 

Materials: 

• 1 standard 10-foot length of 1/2 inch PVC pipe for 180°F water. 

• Flexible meter stick 

• PVC pipe cutter or a hacksaw 

• Sandpaper 

• Seven different colors of permanent markers for labeling pipes 


Directions: 

1. Cut the PVC pipe into the lengths listed in the chart below. It works best if you measure one length, cut it, 

then make the next measurement. You may want to cut each piece a little longer than the given measurement 

so that you can sand out any rough spots and level the pipe without making it too short. 

Number Note Length of pipe (cm) Frequency (Hertz) 

1 F 23.60 349 

2 G 21.00 392 

3 A 18.75 440 

4 B flat 17.50 446 

5 C 15.80 523 

6 D 14.00 587 

7 E 12.50 659 

8 F 11.80 698 

9 G 10.50 748 

10 A 9.40 880 

11 B flat 9.20 892 

12 C 7.90 1049 

13 D 7.00 1174 

14 E 6.25 1318 

15 F 5.90 1397 

2. Lightly sand the cut ends to smooth any rough spots. 

3. Label each pipe with the number, note, and frequency using a different color permanent marker. 

4. Hit one open end of the pipe on the palm of your hand in order to make a sound. 

24.3

Page 2 of 3 

Activities: 

1. Try blowing across the top of a pipe as if you were playing a flute. Does the pipe sound the same as 

when you tap it on your palm? Why or why not? 

24.3 

Safety note: Wash the pipes with rubbing alcohol or a solution of 2 teaspoons household bleach per gallon 

of water before and after blowing across them. 

2. Take one of the longer pipes and place it in a bottle of water so that the top of the pipe extends above the top 

of the bottle. Blow across it like a flute. What happens to the tone as you raise or lower the pipe in the bottle? 

3. Try making another set of palm pipes out of 1/2-inch copper tubing. What happens when you strike these 

pipes against your palm? What happens when you blow across the top? How does the sound compare with 

the plastic pipes? 

4. At a hardware store, purchase two rubber rings for each copper pipe. These rings should fit snugly around 

the pipes. Place one ring on each end of each pipe, then lay them on a table. Try tapping the side of each pipe 

with different objects—wooden and stainless steel serving spoons, for example. How does this sound 

compare with the other sounds you have made with the pipes? 

5. Try playing some palm pipe music with your classmates. Here are two tunes to get you started: 

Happy Birthday 

Melody C C D C F E C C D C G F 

Harmony A A B b B b B b A 

Melody C C C A F E D B b B b A F G F 

Harmony F C B b C A 

Twinkle Twinkle Little Star 

Melody F F C C D D C B b B b A A G G F 

Harmony C C A A B b B b A G G F F E E C 

Melody C C B b B b A A G C C B b B b A A G 

Harmony A A G G F F C A A G G F F C 

Melody F F C C D D C B b B b A A G G F 

Harmony C C A A B b B b A G G F F E E C

Page 3 of 3 

6. Challenge: 

You can figure out the length of pipe needed to make other notes, too. All you need is a simple 

formula and your understanding of the way sound travels in waves. 

To figure out the length of the pipe needed to create sound of a certain frequency, we start with the formula 

frequency = velocity of sound in air ÷ wavelength, or f = v /λ. Next, we solve the equation for λ: λ = v/f. 

The fundamental frequency is the one that determines which note is heard. You can use the chart below to 

find the fundamental frequency of a chromatic scale in two octaves. Notice that for each note, the frequency 

doubles every time you go up an octave. 

Once you choose the frequency of the note you want to play, you need to know what portion of the 

fundamental frequency’s wavelength (S-shape) will fit inside the palm pipe. 

To help you visualize the wave inside the palm pipe, hold the center of a flexible meter stick in front of you. 

Wiggle the meter stick to create a standing wave. This mimics a column of vibrating air in a pipe with two 

open ends. How much of a full wave do you see? If you answered one half, you are correct. 

When a palm pipe is played, your hand closes one end of the pipe. Now use your meter stick to mimic this 

situation. Place the meter stick on a table top and use one hand to hold down one end of the stick. This 

represents the closed end of the pipe. Flick the other end of the meter stick to set it in motion. How much of 

a full wavelength do you see? Now do you know what portion of the wavelength will fit into the palm pipe? 

One-fourth of the wavelength of the fundamental frequency will fit inside the palm pipe. As a result the 

length of the pipe should be equal to 1/4λ, which is equal to 1/4(v/f). 

In practice, we find that the length of pipe needed to make a certain frequency is actually a bit shorter than 

this. Subtracting a length equal to 1/4 of the pipe’s inner diameter is necessary. The final equation, therefore, 

is: Length of pipe 

v 1 

= 

---- – --D where D represents the inner diameter of the pipe. 

4f 4 

Given that the speed of sound in air (at 20 °C) is 343 m/s and the inner diameter of the pipe is 0.0017 m, 

what is the length of pipe you would need to make the note B, with a frequency of 494 hertz? How about the 

same note one octave higher (frequency 988 hertz)? Make these two pipes so that you can play a C major 

scale. 

Chromatic scale in two octaves (frequencies rounded to nearest whole number) 

Note A A# B C C# D D# E F F# G G# A 

Frequency 

(Hertz) 

220 233 247 262 277 294 311 330 349 370 392 415 440 

Frequency 

(Hertz) 

440 466 494 523 554 587 622 659 698 740 784 831 880 

7. What is the lowest note you could make with a palm pipe? What is the highest? Explain these limits using 

what you know about the human ear and the way sound is created by the palm pipe. 

24.3

Name: Date: 

25.1 The Electromagnetic Spectrum 

Radio waves, microwaves, visible light, and x-rays are familiar kinds of electromagnetic waves. All of these 

waves have characteristic wavelengths and frequencies. Wavelength is measured in meters. It describes the length 

of one complete oscillation. Frequency describes the number of complete oscillations per second. It is measured 

in hertz, which is another way of saying “cycles per second.” The higher the wave’s frequency, the more energy 

it carries. 

Frequency, wavelength, and speed 

In a vacuum, all electromagnetic waves travel at the same speed: 3.0 × 10 8 m/s. This quantity is often called “the 

speed of light” but it really refers to the speed of all electromagnetic waves, not just visible light. It is such an 

important quantity in physics that it has its own symbol, c. 

The speed of light is related to 

frequency f and wavelength λ 

by the formula to the right. 

The different colors of light 

that we see correspond to 

different frequencies. The 

frequency of red light is lower 

than the frequency of blue 

light. Because the speed of both kinds of light is the same, a lower frequency wave has a longer wavelength. A 

higher frequency wave has a shorter wavelength. Therefore, red light’s wavelength is longer than blue light’s. 

When we know the frequency of light, the wavelength is given by: λ = 

When we know the wavelength of light, the frequency is given by: f = 

c 

- 

f 

-- 

c 

λ 

25.1

Page 2 of 2 

Answer the following problems. Don’t forget to show your work. 

1. Yellow light has a longer wavelength than green light. Which color of light has the higher frequency? 

2. Green light has a lower frequency than blue light. Which color of light has a longer wavelength? 

3. Calculate the wavelength of violet light with a frequency of 750 × 10 12 Hz. 

4. Calculate the frequency of yellow light with a wavelength of 580 × 10 –9 m. 

5. Calculate the wavelength of red light with a frequency of 460 × 10 12 Hz. 

6. Calculate the frequency of green light with a wavelength of 530 × 10 –9 m. 

7. One light beam has wavelength, λ 1, and frequency, f 1. Another light beam has wavelength, λ 2, and 

frequency, f 2. Write a proportion that shows how the ratio of the wavelengths of these two light beams is 

related to the ratio of their frequencies. 

8. The waves used by a microwave oven to cook food have a frequency of 2.45 gigahertz (2.45 × 10 9 Hz). 

Calculate the wavelength of this type of wave. 

9. A radio station has a frequency of 90.9 megahertz (9.09 × 10 7 Hz). What is the wavelength of the radio 

waves the station emits from its radio tower? 

10. An x-ray has a wavelength of 5 nanometers (5.0 × 10 –9 m). What is the frequency of x-rays? 

11. The ultraviolet rays that cause sunburn are called UV-B rays. They have a wavelength of approximately 300 

nanometers (3.0 × 10 –7 m). What is the frequency of a UV-B ray? 

12. Infrared waves from the sun are what make our skin feel warm on a sunny day. If an infrared wave has a 

frequency of 3.0 × 10 12 Hz, what is its wavelength? 

13. Electromagnetic waves with the highest amount of energy are called gamma rays. Gamma rays have 

wavelengths of less than 10-trillionths of a meter (1.0 × 10 –11 m). 

a. Determine the frequency that corresponds with this wavelength. 

b. Is this the minimum or maximum frequency of a gamma ray? 

14. Use the information from this sheet to order the following types of waves from lowest to highest frequency: 

visible light, gamma rays, x-rays, infrared waves, ultraviolet rays, microwaves, and radio waves. 

15. Use the information from this sheet to order the following types of waves from shortest to longest 

wavelength: visible light, gamma rays, x-rays, infrared waves, ultraviolet rays, microwaves, and radio 

waves. 

25.1

Name: Date: 

25.2 Color Mixing with Additive and Subtractive Processes 

The way that color appears on a piece of paper and how your eyes interpret color involve two different color 

mixing processes. Your eyes see color using an additive color process. The RGB color model is the basis for how 

the additive process works and involves mixing colors of light. The CMYK color model is the basis for how the 

subtractive color process works and involves pigments of color which absorb colors of light. 

RGB color model CMYK color model 

Primary colors Mixed colors New color Primary colors Mixed colors New color 

red red + green yellow magenta magenta + yellow red 

green green + blue cyan yellow yellow + cyan green 

blue blue + red magenta cyan cyan + magenta blue 

How black is 

made 

How white is 

made 

• The human eye has photoreceptors for red, green, and blue light. Which of these photoreceptors are 

stimulated when looking at white paint? 

Solution: All three of these photoreceptors are stimulated equally. 

• A laser printer prints a piece of paper that includes black lettering and a blue border. How are these colors 

made using the CMYK color model? 

Solution: Pure black pigment is used to make the black lettering. If you were to mix the other colors 

(magenta, yellow, and cyan), you would only get a muddy gray. The blue border was made by mixing cyan 

and magenta pigments. 

1. A friend asks you to describe the difference between the RGB color model and the CMYK color model. 

Give him three differences between these color models. 

2. How would you see the following combinations of light colors? 

a. red only 

b. blue + red, both at equal intensity 

c. green only 

d. green + blue, both at equal intensity 

Absence of light How black is 

made 

red + green + blue How white is 

made 

Pure black pigment 

Absence of pigment or use of pure 

white pigment 

3. The color orange is perceived by the eyes when both the red and green photoreceptors are stimulated and the 

red signal is stronger than the green. Given this information, what kind of signals would be received by the 

eye for the color purple? 

25.2

Page 2 of 2 

4. You see a chair that is painted yellow. Most likely, pure yellow pigment was used to make the paint. 

However, explain how your eyes interpret the color yellow. 

5. White paint purchased at a store is often made of a pure white pigment called titanium dioxide. This 

white paint reflects about 97% of the light that strikes it. Why might this property of the paint mean that you 

interpret its color as white? 

6. The image you see on a color TV screen is made using the RGB color model. The image is made of 

thousands of pixels or dots of color. Describe how you could make the following pixels using the RGB color 

model. 

a. A white pixel 

b. A black pixel 

c. A cyan pixel 

d. A yellow pixel 

7. What colors of light are reflected and/or absorbed by a red apple when: 

a. white light shines on it? 

b. only red light shines on it? 

c. only blue light shines on it? 

8. The CMYK color model works because the combination of pigments absorb and reflect light. Imagine that 

white light containing a mixture of red, green, and blue light shines on the combination of CMYK pigments 

in the table below. Copy the table on your own paper. Indicate in the blank spaces which colors of light the 

pigments absorb and which color is reflected. Some parts of the table are filled in for you. 

Mixed colors Reflected color 

CMYK color model 

Which colors of light are absorbed? 

magenta + yellow red 

yellow + cyan 

cyan + magenta 

blue is absorbed by yellow 

red is absorbed by cyan 

9. If you mix magenta paint and cyan paint, what color will you achieve? 

10. A laser printer’s ink only includes the colors cyan, magenta, yellow, and black. 

a. Explain how it makes the color green using these pigments. 

b. Then, explain what happens for your eye to interpret this color as 

green. 

c. This Venn diagram illustrates color mixing for the CMYK color 

model. Now, make a Venn diagram for the RGB color model. Use 

color when you make your diagram. Be sure to label the difference 

between the primary colors and the new colors made by mixing. 

25.2

Name: Date: 

25.2 The Human Eye 

Write the name of the part that corresponds to each letter in the diagram. Then write the function of 

each part in the spaces on the next page. 

25.2

Page 2 of 2 

a. ______________________________________________________________________________ 

b. ______________________________________________________________________________ 

c. ______________________________________________________________________________ 

d. ______________________________________________________________________________ 

e. ______________________________________________________________________________ 

f. ______________________________________________________________________________ 

g. ______________________________________________________________________________ 

h. ______________________________________________________________________________ 

i. ______________________________________________________________________________ 

j. ______________________________________________________________________________ 

k. ______________________________________________________________________________ 

25.2

Name: Date: 

25.3 Measuring Angles with a Protractor 

Measure each of these angles (A–Q) with a protractor. Record the angle measurements in the table 

below. 

Letter Angle Letter Angle 

A J 

B K 

C L 

D M 

E N 

F O 

G P 

H Q 

I 

25.3

Name: Date: 

25.3 Using Ray Diagrams 

This skill sheet gives you some practice using ray diagrams. A ray diagram helps you determine where an image 

produced by a lens will form and shows whether the image is upside down or right side up. 

1. Of the diagrams below, which one correctly illustrates how light rays come off an object? Explain your 

answer. 

2. Of the diagrams below, which one correctly illustrates how a light ray enters and exits a piece of thick glass? 

Explain your answer. 

In your own words, explain what happens to light as it enters glass from the air. Why does this happen? Use 

the term refraction in your answer. 

3. Of the diagrams below, which one correctly illustrates how parallel light rays enter and exit a converging 

lens? Explain your answer. 

4. Draw a diagram of a converging lens that has a focal length of 10 centimeters. In your diagram, show three 

parallel lines entering the lens and exiting the lens. Show the light rays passing through the focal point of the 

lens. Be detailed in your diagram and provide labels. 

25.3

Name: Date: 

25.3 Reflection 

You have seen the law of reflection at work using light and the smooth surface of a mirror. Did you know you 

can apply this law to other situations? It can help you win a game of pool or pass a basketball to a friend on the 

court. 

In this skill sheet you will review the law of reflection and work on practice problems that utilize this law. Use a 

protractor to make your angles correct in your diagrams. 

The law of reflection states that when an object hits a surface, its angle 

of incidence will equal the angle of reflection. This is true when the 

object is light and the surface is a flat, smooth mirror. When the object 

and the surface are larger and lack smooth surfaces (like a basketball 

and a gym floor), the angles of incidence and reflection are nearly but 

not always exactly equal. The angles are close enough that 

understanding the law of reflection can help you improve your game. 

A light ray strikes a flat mirror with a 30-degree angle of incidence. Draw a ray diagram to show how the light 

ray interacts with the mirror. Label the normal line, the incident ray, and the reflected ray. 

Solution: 

1. When we talk about angles of incidence and reflection, we often talk about the normal. The normal to a 

surface is an imaginary line that is perpendicular to the surface. The normal line starts where the incident ray 

strikes the mirror. A normal line is drawn for you in the sample problem above. 

a. Draw a diagram that shows a mirror with a normal line and a ray of light hitting the mirror at an angle of 

incidence of 60 degrees. 

b. In the diagram above, label the angle of reflection. How many degrees is this angle of reflection? 

25.3

Page 2 of 2 

2. Light strikes a mirror’s surface at 20 degrees to the normal. What will the angle of reflection be? 

3. A ray of light strikes a mirror. The angle formed by the incident ray and the reflected ray measures 

90 degrees. What are the measurements of the angle of incidence and the angle of reflection? 

4. In a game of basketball, the ball is bounced (with no spin) toward a player at an angle of 40 degrees to the 

normal. What will the angle of reflection be? Draw a diagram that shows this play. Label the angles of 

incidence and reflection and the normal. 

Challenge Questions: 

Use a protractor to figure out the angles of incidence and reflection for the following problems. 

5. Because a lot of her opponent’s balls are in the way for 

a straight shot, Amy is planning to hit the cue ball off 

the side of the pool table so that it will hit the 8-ball 

into the corner pocket. In the diagram, show the angles 

of incidence and reflection for the path of the cue ball. 

How many degrees does each angle measure? 

6. You and a friend are playing pool. You are 

playing solids and he is playing stripes. You 

have one ball left before you can try for the 

eight ball. Stripe balls are in the way. You 

plan on hitting the cue ball behind one of the 

stripe balls so that it will hit the solid ball 

and force it to follow the pathway shown in 

the diagram. Use your protractor to figure 

out what angles of incidence and reflection 

are needed at points A and B to get the solid 

ball into the far side pocket. 

25.3

Name: Date: 

25.3 Refraction 

25.3 

When light rays cross from one material to another they bend. This bending is called refraction. 

Refraction is a useful phenomenon. All kinds of optics, from glasses to camera lenses to binoculars depend on 

refraction. 

If you are standing on the shore looking at a fish in a stream, the fish appears 

to be in a slightly different place than it really is. That’s because light rays 

that bounce off the fish are refracted at the boundary between water and air. If 

you are a hunter trying to spear this fish, you better know about this 

phenomenon or the fish will get away. 

Why do the light rays bend as they cross from water into air? 

A light ray bends because light travels at different speeds in different 

materials. In a vacuum, light travels at a speed of 3 × 10 8 m/s. But when light 

travels through a material, it is absorbed and re-emitted by each atom or 

molecule it hits. This process of absorption and emission slows the light ray’s 

speed. We experience this slowdown as a bend in the light ray. The greater 

the difference in the light ray’s speed through two different materials, the greater the bend in the path of the ray. 

The index of refraction (n) for a material is the ratio of the speed of light in a vacuum to the speed of light in the 

material. 

speed of light in a vacuum 

Index of refraction = speed of light in a material 

The index of refraction for some common materials is given below: 

Material Index of refraction (n) 

Vacuum 1.0 

Air 1.0001 

Water 1.33 

Glass 1.5 

Diamond 2.42 

1. Could the index of refraction for a material ever be less than 1.0? Explain. 

2. Explain why the index of refraction for air (a gas) is smaller than the index of refraction for a solid like glass. 

3. Calculate the speed of light in water, glass, and diamond using the index of refraction and the speed of light 

in a vacuum (3 × 10 8 m/s). 

4. When a light ray moves from water into air, does it slow down or speed up? 

5. When a light ray moves from water into glass, does it slow down or speed up?

Page 2 of 2 

Which way does the light ray bend? 

Now let’s look at some ray diagrams showing refraction. To make a refraction ray 

diagram, draw a solid line to show the boundary between the two materials (water and 

air in this case). Arrows are used to represent the incident and refracted light rays. The 

normal is a dashed line drawn perpendicular to the boundary between the surfaces. It 

starts at the point where the incident ray hits the boundary. 

As you can see, the light ray is bent toward the normal as it crosses from air into water. 

Light rays always bend toward the normal when they move from a low-n to a high-n 

material. The opposite occurs when light rays travel from a high-n to a low-n material. 

These light rays bend away from the normal. 

The amount of bending that occurs depends on the difference in the index of refraction of the two materials. A 

large difference in n causes a greater bend than a small difference. 

1. A light ray moves from water (n = 1.33) to a transparent plastic (polystyrene n = 1.59). Will the light ray 

bend toward or away from the normal? 

2. A light ray moves from sapphire (n = 1.77) to air (n = 1.0001). Does the light ray bend toward or away from 

the normal? 

3. Which light ray will be bent more, one moving from diamond (n = 2.42) to water (n = 1.33), or a ray moving 

from sapphire (n = 1.77) to air (n = 1.0001)? 

4. 

Material Index of refraction (n) 

Helium 1.00004 

Water 1.33 

Emerald 1.58 

Cubic Zirconia 2.17 

The diagrams below show light traveling from water (A) into another material (B). Using the chart above, 

label material B for each diagram as helium, water, emerald, or cubic zirconia. 

25.3

Name: Date: 

25.3 Drawing Ray Diagrams 

A ray diagram helps you see where the image produced by a lens appears. The components of the diagram 

include the lens, the principal axis, the focal point, the object, and three lines drawn from the tip of the object and 

through the lens. These light rays meet at a point and intersect on the other side of the lens. Where the light rays 

meet indicates where the image of the object appears. 

A lens has a focal length of 2 centimeters. An object is placed 4 centimeters to the left of the lens. Follow the 

steps to make a ray diagram using this information. Trace the rays and predict where the image will form. 

Steps: 

• Draw a lens and show the principal axis. 

• Draw a line that shows the plane of the lens. 

• Make a dot at the focal point of the lens on the right and left sides of the lens. 

• Place an arrow (pointing upward and perpendicular to the principle axis) at 4 centimeters on the left side of 

the lens. 

• Line 1: Draw a line from the tip of the arrow that is parallel to the principal axis on the left, and that goes 

through the focal point on the right of the lens. 

• Line 2: Draw a line from the tip of the arrow that goes through the center of the lens (where the plane and 

the principal axis cross). 

• Line 3: Draw a line from the tip of the arrow that goes through the focal point on the left side of the lens, 

through the lens, and parallel to the principal axis on the right side of the lens. 

• Lines 1, 2, and 3 converge on the right side of the lens where the tip of the image of the arrow appears. 

• The image is upside down compared with the object. 

25.3

Page 2 of 2 

25.3 

1. A lens has a focal length of 4 centimeters. An object is placed 8 centimeters to the left of the lens. 

Trace the rays and predict where the image will form. Is the image bigger, smaller, or inverted as compared 

with the object? 

2. Challenge question: An arrow is placed at 3 centimeters to the left of a converging lens. The image appears 

at 3 centimeters to the right of the lens. What is the focal length of this lens? (HINT: Place a dot to the right 

of the lens where the image of the tip of the arrow will appear. You will only be able to draw lines 1 and 2. 

Where does line 1 cross the principal axis if the image appears at 3 centimeters?) 

3. What happens when an object is placed at a distance from the lens that is less than the focal length? Use the 

term virtual image in your answer.

Name: Date: 

26.1 Astronomical Units 

Talking and writing about distances in our solar system can be cumbersome. The Sun and Neptune are on 

average 4,500,000,000 (or four billion, five hundred million) kilometers apart. Earth’s average distance from the 

Sun is 150,000,000 (one hundred fifty million) kilometers. It can be difficult to keep track of all the zeroes in 

such large numbers. And it’s not easy to compare numbers that large. 

Astronomers often switch to astronomical units (abbreviated AU) when describing distances in our solar system. 

One astronomical unit is 150,000,000 km—the same as the distance from Earth to the Sun. 

Neptune is 30 AU from the Sun. Not only is 30 an easier number to work with than 4,500,000,000; but using 

astronomical units allows us to see immediately that Neptune is 30 times as far from the Sun as Earth. 

In this skill sheet, you will practice working with astronomical units. 

• Jupiter is 778 million kilometers from the Sun, on average. Find this distance in astronomical units. 

Solution: Divide 778 million km by 150 million km: 778,000,000 ÷ 150,000,000 = 5.19 AU 

• The average distance from Mars to the Sun is 1.52 AU. Find this distance in kilometers. 

Solution: Multiply 1.52 AU by 150 million km: 1.52 × 150,000,000 = 228,000,000 km 

1. The average distance from Saturn to the Sun is 1.43 billion kilometers. Find this distance in astronomical 

units. 

2. The average distance from Venus to the Sun is 108 million kilometers. Find this distance in astronomical 

units. 

3. Mercury’s average distance from the Sun is 0.387 astronomical units. How far is this in kilometers? 

4. The average distance from Uranus to the Sun is 19.13 astronomical units. How far is this in kilometers? 

5. Is the distance from Earth to the moon more or less than one astronomical unit? How do you know? 

6. Which planet is almost 20 times as far away from the Sun as Earth? 

7. Which planet is less than half as far away from the Sun as Earth? 

8. Which planet is almost twice as far from the Sun as Jupiter? 

9. An unmanned spacecraft launched from Earth has traveled 10 astronomical units in the direction away from 

the Sun. It most recently passed through the orbit of which planet? 

10. An unmanned spacecraft launched from Earth has traveled 0.5 astronomical units toward the Sun. Has it 

passed through the orbit of Venus yet? 

26.1

Name: Date: 

26.1 Gravity Problems 

In this skill sheet, you will practice using proportions as you learn more about the strength of gravity on different 

planets. 

Comparing the strength of gravity on the planets 

Table 1 lists the strength of gravity on each planet in our solar system. We can see more clearly how these values 

compare to each other using proportions. First, we assume that Earth’s gravitational strength is equal to “1.” 

Next, we set up the proportion where x equals the strength of gravity on another planet (in this case, Mercury) as 

compared to Earth. 

1 

x 

= 

Earth gravitational strength Mercury gravitational strength 

1 x 

= 

9.8 N/kg 3.7 N/kg 

(1× 3.7 N/kg) = (9.8 N/kg × x) 

3.7 N/kg 

= x 

9.8 N/kg 

0.38 = 

x 

Note that the units cancel. The result tells us that Mercury’s gravitational strength is a little more than a third of 

Earth’s. Or, we could say that Mercury’s gravitational strength is 38% as strong as Earth’s. 

Now, calculate the proportions for the remaining planets. 

Table 1: The strength of gravity on planets in our solar system 

Planet Strength of gravity 

(N/kg) 

Value compared to Earth’s 

gravitational strength 

Mercury 3.7 0.38 

Venus 8.9 

Earth 9.8 1 

Mars 3.7 

Jupiter 23.1 

Saturn 9.0 

Uranus 8.7 

Neptune 11.0 

Pluto 0.6 

26.1

Page 2 of 2 

How much does it weigh on another planet? 

Use your completed Table 1 to solve the following problems. 

Example: 

• A bowling ball weighs 15 pounds on Earth. How much would this bowling ball weigh on Mercury? 

Weight on Earth 1 

= 

Weight on Mercury 0.38 

1 15 pounds 

= 

0.38 x 

0.38× 15 pounds = x 

x = 5.7 pounds 

1. A cat weighs 8.5 pounds on Earth. How much would this cat weigh on Neptune? 

2. A baby elephant weighs 250 pounds on Earth. How much would this elephant weigh on Saturn? Give your 

answer in newtons (4.48 newtons = 1 pound). 

3. On Pluto, a baby would weigh 2.7 newtons. How much does this baby weigh on Earth? Give your answer in 

newtons and pounds. 

4. Imagine that it is possible to travel to each planet in our solar system. After a space “cruise,” a tourist returns 

to Earth. One of the ways he recorded his travels was to weigh himself on each planet he visited. Use the list 

of these weights on each planet to figure out the order of the planets he visited. On Earth he weighs 

720 newtons. List of weights: 655 N; 1,699 N; 806 N; 43 N; and 662 N. 

Challenge: Using the Universal Law of Gravitation 

Here is an example problem that is solved using 

the equation for Universal Gravitation. 

Example 

What is the force of gravity between Pluto and 

Earth? The mass of Earth is 6.0 × 10 24 kg. The 

mass of Pluto is 1.3 × 10 22 kg. The distance 

between these two planets is 5.76 × 10 12 meters. 

Force of gravity between Earth and Pluto 

Now use the equation for Universal Gravitation to solve this problem: 

6.67 10 -11 

× N-m 2 

kg 2 

⎛ ⎞ 

⎜------------------------------------------ 6.0 10 

⎟ 

⎝ ⎠ 

24 

( × kg) 

1.3 10 22 

× ( × kg) 

5.76 10 12 

( × m) 

2 

= 

----------------------------------------------------------------------------- 

Force of gravity 

52.0 10 35 

× 

33.2 10 24 

-------------------------- 1.57 10 

× 

11 = = 

× N 

5. What is the force of gravity between Jupiter and Saturn? The mass of Jupiter is 6.4 × 10 24 kg. The mass of 

Saturn is 5.7 × 10 26 kg. The distance between Jupiter and Saturn is 6.52 × 10 11 m. 

26.1

Name: Date: 

26.1 Universal Gravitation 

The law of universal gravitation allows you to calculate the gravitational force between two objects from their 

masses and the distance between them. The law includes a value called the gravitational constant, or “G.” This 

value is the same everywhere in the universe. Calculating the force between small objects like grapefruits or huge 

objects like planets, moons, and stars is possible using this law. 

What is the law of universal gravitation? 

The force between two masses m 1 and m 2 that are separated by a distance r is given by: 

So, when the masses m 1 and m 2 are given in kilograms and the distance r is given in meters, the force has the 

unit of newtons. Remember that the distance r corresponds to the distance between the center of gravity of 

the two objects. 

For example, the gravitational force between two spheres that are touching each other, each with a radius of 

0.300 meter and a mass of 1,000. kilograms, is given by: 

F 6.67 10 11 

× 1,000. kg 1,000. kg 

= 

– N-m 2 kg 2 

⁄ 

× 

( 0.300 m + 0.300 m) 

2 

---------------------------------------------------- = 0.000185 N 

Note: A small car has a mass of approximately 1,000. kilograms. Try to visualize this much mass 

compressed into a sphere with a diameter of 0.300 meters (30.0 centimeters). If two such spheres were 

touching one another, the gravitational force between them would be only 0.000185 newtons. On Earth, this 

corresponds to the weight of a mass equal to only 18.9 milligrams. The gravitational force is not very strong! 

26.1

Page 2 of 2 

Answer the following problems. Write your answers using scientific notation. 

1. Calculate the force between two objects that have masses of 70. kilograms and 2,000. kilograms. Their 

centers of gravity are separated by a distance of 1.00 meter. 

2. Calculate the force between two touching grapefruits each with a radius of 0.080 meters and a mass of 

0.45 kilograms. 

3. Calculate the force between one grapefruit as described above and Earth. Earth has a mass of 

5.9742 × 10 24 kilograms and a radius of 6.3710 × 10 6 meters. Assume the grapefruit is resting on Earth’s 

surface. 

4. A man on the moon with a mass of 90. kilograms weighs 146 newtons. The radius of the moon is 

1.74 × 106 meters. Find the mass of the moon. 

5. For m = 5.9742 × 1024 kilograms and r = 6.3710 × 106 meters, what is the value given by: G ? 

a. Write down your answer and simplify the units. 

b. What does this number remind you of? 

c. What real-life values do m and r correspond to? 

m 

r 2 

---- 

6. The distance between the centers of Earth and its moon is 3.84 × 10 8 meters. Earth’s mass is 

5.9742 × 10 24 kilograms and the mass of the moon is 7.36 × 10 22 kilograms. What is the force between Earth 

and the moon? 

7. A satellite is orbiting Earth at a distance of 35.0 kilometers. The satellite has a mass of 500. kilograms. What 

is the force between the planet and the satellite? Hint: Recall Earth’s mass and radius from earlier problems. 

8. The mass of the sun is 1.99 × 10 30 kilograms and its distance from Earth is 150. million kilometers 

(150. × 10 9 meters). What is the gravitational force between the sun and Earth? 

26.1

Page 1 of 2 

26.1 Nicolaus Copernicus 

Nicolaus Copernicus was a church official, mathematician, and influential astronomer. His 

revolutionary theory of a heliocentric (sun-centered) universe became the foundation of 

modern-day astronomy. 

Wealth, education, and religion 

Nicolaus Copernicus was 

born on February 19, 1473 

in Torun, Poland. 

Copernicus’ father was a 

successful copper merchant. 

His mother also came from 

wealth. Being from a 

privileged family, young 

Copernicus had the luxury 

of learning about art, 

literature, and science. 

When Copernicus was only 

10 years old, his father died. Copernicus went to live 

his uncle, Lucas Watzenrode, a prominent Catholic 

Church official who became bishop of Varmia (now 

part of modern-day Poland) in 1489. The bishop was 

generous with his money and provided Copernicus 

with an education from the best universities. 

From church official to astronomer 

Copernicus lived during the height of the Renaissance 

period when men from a higher social class were 

expected to receive well-rounded educations. In 1491, 

Copernicus attended the University of Krakow where 

he studied mathematics and astronomy. After four 

years of study, his uncle appointed Copernicus a 

church administrator. Copernicus used his church 

wages to help pay for additional education. 

In January 1497, Copernicus left for Italy to study 

medicine and law at the University of Bologna. 

Copernicus’ passion for astronomy grew under the 

influence of his mathematics professor, Domenico 

Maria de Novara. Copernicus lived in his professor’s 

home where they spent hours discussing astronomy. 

In 1500, Copernicus lectured on astronomy in Rome. 

A year later, he studied medicine at the University of 

Padua. In 1503, Copernicus received a doctorate in 

canon (church) law from the University of Ferrara. 

Observations with his bare eyes 

After his studies in Italy, Copernicus returned to 

Poland to live in his uncle’s palace. He resumed his 

church duties, practiced medicine, and studied 

astronomy. Copernicus examined the sky from a 

palace tower. He made his observations without any 

equipment. In the late 1500s, the astronomer Galileo 

used a telescope and confirmed Copernicus’ ideas. 

26.1 

A heliocentric universe 

In the 1500s, most astronomers believed that Earth 

was motionless and the center of the universe. They 

also thought that all celestial bodies moved around 

Earth in complicated patterns. The Greek astronomer 

Ptolomy proposed this geocentric theory more than 

1000 years earlier. 

However, Copernicus believed that the universe was 

heliocentric (sun-centered), with all of the planets 

revolving around the sun. He explained that Earth 

rotates daily on its axis and revolves yearly around the 

sun. He also suggested that Earth wobbles like a top as 

it rotates. 

Copernicus’ theory led to a new ordering of the planets. 

In addition, it explained why the planets farther from 

the sun sometimes appear to move backward 

(retrograde motion), while the planets closest to the sun 

always seem to move in one direction. This retrograde 

motion is due to Earth moving faster around the sun 

than the planets farther away. 

Copernicus was reluctant to publish his theory and 

spent years rechecking his data. Between 1507 and 

1515, Copernicus circulated his heliocentric principles 

to only a few astronomers. A young German 

mathematics professor, George Rheticus, was 

fascinated with Copernicus’ theory. The professor 

encouraged Copernicus to publish his ideas. Finally, 

Copernicus published The Revolutions of the 

Heavenly Orbs near his death in 1543. 

Years later, several astronomers (including Galileo) 

embraced Copernicus’ sun-centered theory. However, 

they suffered much persecution by the church for 

believing such ideas. At the time, church law held 

great influence over science and dictated a geocentric 

universe. It wasn’t until the eighteenth century that 

Copernicus’ heliocentric principles were completely 

accepted.

Page 2 of 2 


1. How did Copernicus’ privileged background help him become knowledgeable in so many areas of 

study? 

2. Which people influenced Copernicus in his work as a church official and an astronomer? 

3. How did Copernicus make his observations of the sky? 

4. What did astronomers believe of the universe prior to the sixteenth century? 

5. Describe Copernicus’ revolutionary heliocentric theory of the universe. 

6. Why did so many astronomers face persecution by the church for their beliefs in a heliocentric universe? 

7. Research: Using the library or Internet, find out which organizations developed the Copernicus Satellite 

(OAO-3) and why it was used. 

26.1

Page 1 of 2 

26.1 Galileo Galilei 

Galileo Galilei was a mathematician, scientist, inventor, and astronomer. His observations led to 

advances in our understanding of pendulum motion and free fall. He invented a thermometer, water pump, 

military compass, and microscope. He refined a Dutch invention, the telescope, and used it to revolutionize 

our understanding of the solar system. 

An incurable mathematician 

Galileo Galilei was born in 

Pisa, Italy, on February 15, 

1564. His father, a musician 

and wool trader, hoped his son 

would find a more profitable 

career. He sent Galileo to a 

monastery school at age 11 to 

prepare for medical school. 

After four years there, Galileo 

decided to become a monk. 

The eldest of seven children, 

he had sisters who would need dowries in order to 

marry, and his father had planned on Galileo’s 

support. His father decided to take Galileo out of the 

monastery school. 

Two years later, he enrolled as a medical student at the 

University of Pisa, though his interests were 

mathematics and natural philosophy. Galileo did not 

really want to pursue medical studies. Eventually, his 

father agreed to let him study mathematics. 

Seeing through the ordinary 

Galileo was extremely curious. At 20, he found 

himself watching a lamp swinging from a cathedral 

ceiling. He used his pulse like a stopwatch and 

discovered that the lamp’s long and short swings took 

the same amount of time. He wrote about this in an 

early paper titled “On Motion.” Years later, he drew 

up plans for an invention, a pendulum clock, based on 

this discovery. 

Inventions and experiments 

Galileo started teaching at the University of Padua in 

1592 and stayed for 18 years. He invented a simple 

thermometer, a water pump, and a compass for 

accurately aiming cannonballs. He also performed 

experiments with falling objects, using an inclined 

plane to slow the object’s motion so it could be more 

accurately timed. Through these experiments, he 

realized that all objects fall at the same rate unless 

acted on by another force. 

26.1 

Crafting better telescopes 

In 1609, Galileo heard that a Dutch eyeglass maker 

had invented an instrument that made things appear 

larger. Soon he had created his own 10-powered 

telescope. The senate in Venice was impressed with its 

potential military uses, and in a year, Galileo had 

refined his invention to a 30-powered telescope. 

Star gazing 

Using his powerful telescope, Galileo’s curiosity now 

turned skyward. He discovered craters on the moon, 

sunspots, Jupiter’s four largest moons, and the phases 

of Venus. His observations led him to conclude that 

Earth could not possibly be the center of the universe, 

as had been commonly accepted since the time of the 

Greek astronomer Ptolemy in the second century. 

Instead, Galileo was convinced that Polish astronomer 

Nicolaus Copernicus (1473-1543) must have been 

right: The Sun is at the center of the universe and the 

planets revolve around it. 

House arrest 

The Roman Catholic Church held that Ptolemy’s 

theory was truth and Copernican theory was heresy. 

Galileo had been told by the Inquisition in 1616 to 

abandon Copernican theory and stop pursuing these 

ideas. 

Despite these threats, in February 1632, he published 

his ideas in the form of a conversation between two 

characters. He made the one representing Ptolemy’s 

view seem foolish, while the other, who argued 

Copernicus’s theory, seemed wise. 

This angered the church, whose permission was 

needed for publishing books. Galileo was called to 

Rome before the Inquisition. He was given a formal 

threat of torture and so he abandoned his ideas that 

promoted Copernican theory. He was sentenced to 

house arrest, and lived until his death in 1642 watched 

over by Inquisition guards.

Page 2 of 2 


1. What scientific information was presented in Galileo’s paper “On Motion”? 

2. Research one of Galileo’s inventions and draw a diagram showing how it worked. 

3. How were Galileo’s views about the position of Earth in the universe supportive of Copernicus’s ideas? 

4. Imagine you could travel back in time to January 1632 to meet with Galileo just before he publishes his 

“Dialogue Concerning the Two Chief World Systems.” What would you say to him? 

5. In your opinion, which of Galileo’s ideas or inventions had the biggest impact on history? Why? 

26.1

Page 1 of 2 

26.1 Johannes Kepler 

26.1 

Johannes Kepler was a mathematician who studied astronomy. He lived at the same time as two other 

famous astronomers, Tycho Brahe and Galileo Galilei. Kepler is recognized today for his use of mathematics to 

solve problems in astronomy. Kepler explained that the orbit of Mars and other planets is an ellipse. In his most 

famous books he defended the sun-centered universe and his three laws of planetary motion. 

Early years in Germany 

Johannes Kepler was born 

December 27, 1571, in Weil 

der Stadt, Wurttemburg, 

Germany, now called the 

“Gate to the Black Forest.” 

He was the oldest of six 

children in a poor family. 

As a child he lived and 

worked in an inn run by his 

mother’s family. He was 

sickly, nearsighted, and 

suffered from smallpox at a 

young age. Despite his physical condition, he was a 

bright student. 

The first school Kepler attended was a convent school 

in Adelberg monastery. Kepler’s original plan was to 

study to become a Lutheran minister. In 1589, Kepler 

received a scholarship to attend the University of 

Tubingen. There he spent three years studying 

mathematics, philosophy, and theology. His interest in 

math led him to take a mathematics teaching position 

at the Academy in Graz. There he began teaching and 

studying astronomy. 

Influenced by Copernicus 

At Tubingen, Kepler’s professor, Michael Mastlin, 

introduced Kepler to Copernican astronomy. 

Nicholaus Copernicus (1473-1543), had published a 

revolutionary theory in, “On the Revolutions of 

Heavenly Bodies.” Copernicus’ theory stated that the 

sun was the center of the solar system. Earth and the 

planets rotated around the sun in circular orbits. At the 

time most people believed that Earth was the center of 

the universe. 

Copernican theory intrigued Kepler and he wrote a 

defense of it in 1596, Mysterium Cosmographicum. 

Although Kepler’s original defense was flawed, it was 

read by several other famous European astronomers of 

the time, Tycho Brahe (1546–1601) and Galileo 

Galilei (1546–1642). 

Kepler published many books in which he explained 

how vision, optics, and telescopes work. His most 

famous work, though, dealt with planetary motion. 

Working with Tyco Brahe 

In 1600, Brahe invited Kepler to join him. Brahe, 

a Danish astronomer, was studying in Prague, 

Czechoslovakia. Every night for years Brahe recorded 

planetary motion without a telescope from his 

observatory. Brahe asked Kepler to figure out a 

scientific explanation for the motion of Mars. Less 

than two years later, Brahe died. Kepler was awarded 

Brahe’s position as Imperial Mathematician. He 

inherited Brahe’s collection of planetary observations 

to use to write mathematical descriptions of planetary 

motion. 

Kepler’s Laws of Planetary Motion 

Kepler discovered that Mars’ orbit was an ellipse, not 

a circle, as Copernicus had thought. Kepler published 

his first two laws of planetary motion in Astronomia 

Nova in 1609. The first law of planetary motion stated 

that planets orbit the sun in an elliptical orbit with the 

sun in one of the foci. The second law, the law of 

areas, said that planets speed up as their orbit is closest 

to the sun, and slow down as planets move away from 

the sun. Kepler published a third law, called the 

harmonic law, in 1619. The third law shows how a 

planet’s distance from the sun is related to the amount 

of time it takes to revolve around the sun. His work 

influenced Isaac Newton’s later work on gravity. 

Kepler’s calculations were done before calculus was 

invented! 

Other scientific discoveries 

Kepler sent his book in 1609 to Galileo. Galileo’s 

theories did not agree with Kepler’s ideas and the two 

scientists never worked together. Despite his 

accomplishments, when Kepler died at age 59, he was 

poor and on his way to collect an old debt. It would 

take close to a century for his work to gain the 

recognition it deserved.

Page 2 of 2 


1. Why was Copernicus’ idea of the sun at the center of the solar system considered revolutionary? 

2. Explain how Brahe helped Kepler make important discoveries in astronomy. 

3. How was Kepler’s approach to astronomy different than Brahe’s and Galileo’s? 

4. Kepler discovered that Mars and other planets traveled in an ellipse around the sun. Does this agree with 

Copernicus’ theory? 

5. Describe Kepler’s three laws of planetary motion. 

6. Kepler observed a supernova in 1604. It challenged the way people at the time thought about the universe 

because people did not know the universe could change. When people have to change their beliefs about 

something because scientific evidence says otherwise, that is called a “paradigm shift.” Find three examples 

in the text of scientific discoveries that led to a “paradigm shift.” 

26.1

Name: Date: 

26.1 Measuring the Moon’s Diameter 

In this skill sheet you will explore how to measure the moon’s diameter using simple tools and calculations. 

Materials 

Here are the materials you will need to measure the moon’s diameter: 

• A 3-meter piece of string • Scissors 

• A metric tape measure • Marker 

• A small metric ruler • One-centimeter semi-circle card (Cut out from the 

bottom of the last page) 

• Tape 

Proportions and geometry 

The method you will use to measure the moon’s diameter depends on the properties of similar triangles. The 

following exercise demonstrates these properties. 

Below is a large triangle. A line drawn from one side to the other of the large triangle results in a smaller triangle 

inside the larger one. The ends of each line are labeled with letters. 

1. Make the following measurements of the lines on the triangle: 

Distance AC: ____________________ cm 

Distance AD: ____________________ cm 

Distance AB: ____________________ cm 

Distance AE: ____________________ cm 

Distance BE: ____________________ cm 

Distance CD: ____________________ cm 

26.1

Page 2 of 3 

2. How is the distance from AB related to AC? 

3. How is the distance from BE related to CD? 

4. Based on your measurements and your answers to questions (2) and (3), come up with a statement 

that explains the properties of similar triangles. 

Finding the diameter of the moon 

Now, you are ready to use your supplies to find the diameter of the moon. Follow these steps carefully and 

answer the questions as you go. 

1. Locate a place where you can see the moon from a window. This is possible at night or early in the morning. 

2. Use scissors to carefully cut out the semi-circle card found on the next page. 

3. Tape this card to the window when you can see the full (or gibbous) moon through the window. 

4. Tape one end of the 3-meter piece of string to the card directly underneath the semi-circle. 

5. Now, slowly move backward from the window while holding on to the string. Watch your step! As you 

move backward, pay attention to the moon. You want to move back far enough so that the bottom half of the 

moon “sits” in the semi-circle cutout. You want the semi-circle to be the same size as the lower half to the 

moon. 

6. When the lower half of the moon is the same size as the semi-circle cut out, stop moving backward and hold 

the string up to the side of one of your eyes. Have a friend carefully mark the string at this distance. 

7. Now, measure the distance from the window to the mark on the string to the nearest millimeter. Convert this 

distance to meters. Write the string distance in Table 1. 

Table 1:Finding the moon’s diameter data 

Semi-circle diameter 0.01 meter 

String distance 

Diameter of the moon ??? 

Distance from Earth to the moon 384, 400, 000 meters 

Finding the moon’s diameter 

1. You have three out of four measurements in Table 1. The only measurement you need is the moon’s 

diameter. You can find the moon’s diameter using proportions. Which calculation will help you? 

a. b. 

semi-circle 

----------------------------------------------diameter 

moon diameter 

c. d. 

----------------------------------------------moon 

diameter 

semi-circle diameter 

= 

= 

---------------------------------------------------------------------------distance 

to semi-circle 

distance from Earth to the moon 

---------------------------------------------------------------------------distance 

to semi-circle 


---------------------------------------------------semi-circle 

diameter 

distance to semi-circle 

----------------------------------------------moon 

diameter 

semi-circle diameter 

2. Use the proportion that you selected in question (1) to calculate the moon’s diameter. 

3. How is performing this calculation like the exercise you did in part 2? 

= 

= 

---------------------------------------------------------------------------moon 

diameter 


distance---------------------------------------------------------------------------from 

Earth to the moon 

distance to semi-circle 

26.1

Page 3 of 3 

Semi-Circle Card: 

26.1

Page 1 of 2 

26.2 Benjamin Banneker 

Benjamin Banneker was a farmer, naturalist, civil rights advocate, self-taught mathematician, 

astronomer and surveyor who published his detailed astronomical calculations in popular almanacs. 

He was appointed by President George Washington as one of three surveyors of the territory that 

became Washington D.C. 

Early times 

Benjamin Banneker was born 

in rural Maryland in 1731. His 

family was part of a 

population of about two 

hundred free black men and 

women in Baltimore county. 

They owned a small farm 

where they grew tobacco and 

vegetables, earning a 

comfortable living. 

A mathematician builds a clock 

Benjamin’s grandmother taught him to read, and he 

briefly attended a Quaker school near his home. 

Benjamin enjoyed school and was especially fond of 

solving mathematical riddles and puzzles. When he 

was 22, Benjamin borrowed a pocket watch, took it 

apart, and made detailed sketches of its inner 

workings. Then he carved a large-scale wooden model 

of each piece, fashioned a homemade spring, and built 

his own clock that kept accurate time for over 

50 years. 

A keen observer of the night sky 

As a young adult, Benjamin designed an irrigation 

system that kept his family farm prosperous even in 

dry years. The Bannekers sold their produce at a 

nearby store owned by a Quaker family, the Ellicotts. 

There, Benjamin became friends with George Ellicott, 

who loaned him books about astronomy and 

mathematics. 

Banneker was soon recording detailed observations of 

the night sky. He performed complicated calculations 

to predict the positions of planets and the timing of 

eclipses. From 1791 to 1797, Banneker published his 

astronomical calculations along with weather and tide 

predictions, literature, and commentaries in six 

almanacs. The almanacs were widely read in 

Maryland, Delaware, Pennsylvania, and Virginia, 

bringing Banneker a measure of fame. 

26.2 

A keen observer of nature 

Banneker was also a keen observer of the natural 

world and is believed to be the first person to 

document the cycle of the 17-year cicada, an insect 

that exists in the larval stage underground for 17 years, 

and then emerges to live for just a few weeks as a loud 

buzzing adult. 

Banneker writes Thomas Jefferson 

Banneker sent a copy of his first almanac to then- 

Secretary of State Thomas Jefferson, along with a 

letter challenging Jefferson’s ownership of slaves as 

inconsistent with his assertion in the Declaration of 

Independence that “all men are created equal.” 

Jefferson sent a letter thanking Banneker for the 

almanac, saying that he sent it onto the Academy of 

Sciences of Paris as proof of the intellectual 

capabilities of Banneker’s race. Although Jefferson’s 

letter stated that he “ardently wishes to see a good 

system commenced for raising the condition both of 

[our black brethren’s] body and mind,” regrettably, he 

never freed his own slaves. 

Designing Washington D.C. 

In 1791, George Ellicott’s cousin Andrew Ellicott 

asked him to serve as an astronomer in a large 

surveying project. George Ellicott suggested that he 

hire Benjamin Banneker instead. 

Banneker left his farm in the care of relatives and 

traveled to Washington, where he became one of three 

surveyors appointed by President George Washington 

to assist in the layout of the District of Columbia. 

After his role in the project was complete, Banneker 

returned to his Maryland farm, where he died in 1806. 

Banneker Overlook Park, in Washington D.C., 

commemorates his role in the surveying project. In 

1980, the U.S. Postal Service issued a stamp in 

Banneker’s honor.

Page 2 of 2 


1. Benjamin Banneker built a working clock that lasted 50 years. Why would his understanding of 

mathematics have been helpful in building the clock? 

2. Identify one of Banneker’s personal strengths. Justify your answer with examples from the reading. 

3. Benjamin Banneker lived from 1731 to 1806. During his lifetime, he advocated equal rights for all people. 

Find out the date for each of the following “equal rights” events: (a) the Emacipation Proclamation, (b) the 

end of the Civil War, (c) women gain the right to vote, and (d) the desegregation of public schools (due to 

the landmark Supreme Court case, Brown versus the Board of Education). 

4. Name three of Benjamin Banneker’s lifetime accomplishments. 

5. What do you think motivated Banneker during his lifetime? What are some possible reasons that he was 

persistent in his scientific work? 

6. Research: Find a mathematical puzzle written by Banneker. Try to solve it with your class. 

26.2

Name: Date: 

26.3 Touring the Solar System 

What would a tour of our solar system be like? How long would it take? How much food would you have to 

bring? In this skill sheet, you will calculate the travel times for an imaginary tour of the solar system. For our 

purposes, we will pretend that the planets form one straight line away from the Sun. Your mode of transportation 

will be a space vehicle travelling at 250 meters per second or 570 miles per hour. 

Part 1: Planets on the tour 

Starting from Earth, the tour itinerary is: Earth to Mars to Saturn to Neptune to Venus and then back to Earth. 

The distances between each planet of the tour are provided in Table 1. The space vehicle travels at 250 meters per 

second or 900 kilometers per hour. Using this rate and the speed formula, find out how long it will take to travel 

each leg of the itinerary. An example is provided below. For the table, also calculate the time in days and years. 

• How many days will it take to travel from Earth to Mars if the distance between the planets is 78 million 

kilometers? 

Solution: 

Legs of the trip Distance 

traveled for 

each leg (km) 

Earth to Mars 78,000,000 

Mars to Saturn 1,202,000,000 

Saturn to Neptune 3,070,000,000 

Neptune to Venus 4,392,000,000 

Venus to Earth 42,000,000 

distance 

time = 

speed 

78 million km 

time to travel from Earth to Mars = 

km 

900 

hour 

time to travel from Earth to Mars = 86,666 hours 

1 day 

86,666 hours× = 

3,611 days 

24 hours 

Table 1: Solar System Trip 

Hours 

traveled 

Days 

traveled 

Years 

traveled 

26.3

Page 2 of 2 

Part 2: Provisions for the trip 

A trip through the solar system is a science fiction fantasy. Answer the following questions as if such a 

journey were possible. 

1. It is recommended that a person drink eight glasses of water each day. To keep yourself hydrated on your 

trip. How many glasses of water would you need to drink on the leg from Earth to Mars? 

2. An average person needs 2,000 food calories per day. How many food calories will you need for the leg of 

the journey from Neptune to Venus? 

3. Proteins and carbohydrates provide 4 calories per gram. Fat provides 9 calories per gram. Given this 

information, would it be more efficient to pack the plane full of foods that are high in fat or high in protein 

for the journey? Explain your answer. 

4. You decide that you want to celebrate Thanksgiving each year of your travel. How many frozen turkeys will 

you need for the entire journey? 

Part 3: Planning a trip to all eight planets 

Section 26.3 of your student text presents a table that lists the properties of the eight planets. Use this table to 

answer the following questions. 

1. On which planet would there be the most opportunities to visit a moon? 

2. Which planets would require high-tech clothing to endure high temperatures? Which planets would require 

high-tech clothing to endure cold temperatures? 

3. Which planet has the longest day? 

4. Which has the shortest day? 

5. On which planet would you have the most weight? How much would you weigh in newtons? 

6. Which planet would take the longest time to travel around? 

7. Which planet would require your spaceship to orbit with the fastest orbital speed? Explain your answer. 

26.3

Name: Date: 

27.1 The Sun: A Cross-Section 

27.1

Page 1 of 2 

27.1 Arthur Walker 

27.1 

Arthur Walker pioneered several new space-based research tools that brought about significant 

changes in our understanding of the sun and its corona. He was instrumental in the recruitment and retention of 

minority students at Stanford University, and he advised the United States Congress on physical science policy 

issues. 

Not to be discouraged 

Arthur Walker was born in 

Cleveland in 1936. His father 

was a lawyer and his mother a 

social worker. When he was 5, 

the family moved to New 

York. Arthur was an excellent 

student and his mother 

encouraged him to take the 

entrance exam for the Bronx 

High School of Science. 

Arthur passed the exam, but when he entered school a 

faculty member told him that the prospects for a black 

scientist in the United States were bleak. 

Rather than allow him to become dissuaded from his 

aspirations, Arthur’s mother visited the school and 

told them that her son would pursue whatever course 

of study he wished. 

Making his mark in space 

Walker went on to earn a bachelor’s degree in physics, 

with honors, from Case Institute of Technology in 

Cleveland and, by 1962, his master’s and doctorate 

from the University of Illinois. 

Afterward, he spent three years’ active duty with the 

Air Force, where he designed a rocket probe and 

satellite experiment to measure radiation that affects 

satellite operation. This work sparked Walker’s 

lifelong interest in developing new space-based 

research tools. 

After completing his military service, Walker worked 

with other scientists to develop the first X-ray 

spectrometer used aboard a satellite. This device 

helped determine the temperature and composition of 

the sun’s corona and provided new information about 

how matter and radiation interact in plasma. 

Snapshots of the sun 

In 1974, Walker joined the 

faculty at Stanford 

University. There he 

pioneered the use of a new 

multilayer mirror 

technology in space 

observations. The mirrors 

selectively reflected X rays 

of certain wavelengths, and 

enabled Walker to obtain 

the first high-resolution images showing different 

temperature regions of the solar atmosphere. He then 

worked to develop telescopes using the multilayer 

mirror technology, and launched them into space on 

rockets. The telescopes produced detailed photos of 

the sun and its corona. One of the pictures was 

featured on the cover of the journal Science in 

September 1988. 

A model for student scientists 

Walker was a mentor to many graduate students, 

including Sally Ride, who went on to become the first 

American woman in space. He worked to recruit and 

retain minority applicants to Stanford’s natural and 

mathematical science programs. Walker was 

instrumental in helping Stanford University graduate 

more black doctoral physicists than any university in 

the United States. 

At work in other orbits 

Public service was important to Walker, who served 

on several committees of the National Aeronautics 

and Space Administration (NASA), National Science 

Foundation, and National Academy of Science, 

working to develop policy recommendations for 

Congress. He was also appointed to the presidential 

commission that investigated the 1986 space shuttle 

Challenger accident. 

Walker died of cancer in April 2001.

Page 2 of 2 


1. Use your textbook, an Internet search engine, or a dictionary to find the definition of each word in 

bold type. Write down the meaning of each word. Be sure to credit your source. 

2. What have you learned about pursuing goals from Arthur Walker’s biography? 

3. Why is a spectrometer a useful device for measuring the temperature and composition of something like the 

sun’s corona? 

4. Research: Use a library or the Internet to find one of Walker’s revolutionary photos of the sun and its 

corona. Present the image to your class. 

5. Research: Use a library or the Internet to find more about the commission that investigated the explosion of 

the space shuttle Challenger in 1986. Summarize the commission’s findings and recommendations in two or 

three paragraphs. 

27.1

Name: Date: 

27.2 The Inverse Square Law 

If you stand one meter away from a portable stereo blaring your favorite music, the intensity of the sound may 

hurt your ears. As you back away from the stereo, the sound’s intensity decreases. When you are two meters 

away, the sound intensity is one-fourth its original value. When you are ten meters away, the sound intensity is 

one-one hundredth its original value. 

The sound intensity decreases according to the inverse square law. This means that the intensity decreases as the 

square of the distance. If you triple your distance from the stereo, the sound intensity decreases by nine times its 

original value. 

Many fields follow an inverse square law, including sound, light from a small source (like a match or light bulb), 

gravity, and electricity. Magnetic fields are the exception. They decrease much faster because there are two 

magnetic poles. 

Example 1: The light intensity one meter from a bulb is 2 W/m 2 . What is the light intensity measured from a 

distance of four meters from the bulb? 

Solution: The distance has increased to four times its original value. The light intensity will decrease by 42 or 16, times. 

1 1 

2× = 

or 0.125 W/m 

16 8 

Example 2: Mercury has a gravitational force of 3.7 N/kg. Its radius is 2,439 kilometers. How far away from the 

surface of Mercury would you need to move in order to experience a gravitational force of 0.925 N/kg? 

Solution: For the gravitational force to be reduced to one-fourth its original value, the distance from Mercury’s center 

must be doubled. Therefore you would have to move to a spot 2,439 kilometers away from Mercury’s surface or 4,878 

meters from its center. 

1. You stand 4 meters away from a light and measure the intensity to be 1 W/m 2 . What will be the intensity if 

you move to a position 8 meters away from the bulb? 

2. You are standing 1 meter from a squawking parrot. If you move to a distance three meters away, the sound 

intensity will be what fraction of its original value? 

3. Venus has a gravitational force of 8.9 N/kg. Its radius is 6,051 kilometers. How far away from the surface of 

Mercury would you need to move in order to experience a gravitational force of 0.556 N/kg? 

4. Earth’s radius is 6,378 kilometers. If you weigh 500 newtons on Earth’s surface, what would you weigh at a 

distance of 19,134 kilometers from Earth? 

5. Compare the intensity of light 2 meters away from a lit match to the intensity 6 meters away from the match. 

6. How does the strength of a sound field 1 meter from its source compare with its strength 4 meters away? 

2 

27.2

Name: Date: 

28.1 Scientific Notation 

28.1 

A number like 43,200,000,000,000,000,000 (43 quintillion, 200 quadrillion) can take a long time to 

write, and an even longer time to read. Because scientists frequently encounter very large numbers like this one 

(and also very small numbers, such as 0.000000012, or twelve trillionths), they developed a shorthand method 

for writing these types of numbers. This method is called scientific notation. A number is written in scientific 

notation when it is written as the product of two factors, where the first factor is a number that is greater than or 

equal to 1, but less than 10, and the second factor is an integer power of 10. Some examples of numbers written 

in scientific notation are given in the table below: 


4.32 × 10 19 43,200,000,000,000,000,000 

1.2 × 10 –8 0.000000012 

5.2777 × 10 7 

Rewrite numbers given in scientific notation in standard form. 

52,777,000 

6.99 10 -5 0.0000699 

• Express 4.25 × 10 6 in standard form: 4.25 × 10 6 = 4,250,000 

Move the decimal point (in 4.25) six places to the right. The exponent of the “10” is 6, giving us the number 

of places to move the decimal. We know to move it to the right since the exponent is a positive number. 

• Express 4.033 × 10 –3 in standard form: 4.033 × 10 –3 = 0.004033 

Move the decimal point (in 4.033) three places to the left. The exponent of the “10” is negative 3, giving the 

number of places to move the decimal. We know to move it to the left since the exponent is negative. 

Rewrite numbers given in standard form in scientific notation. 

• Express 26,040,000,000 in scientific notation: 26,040,000,000 = 2.604 × 10 10 


gives the first factor (2.604). To get from 2.604 to 26,040,000,000 the decimal point has to move 10 places to 

the right, so the power of ten is positive 10. 

• Express 0.0001009 in scientific notation: 0.0001009 = 1.009 × 10 –4 


gives the first factor (1.009). To get from 1.009 to 0.0001009 the decimal point has to move four places to 

the left, so the power of ten is negative 4.

Page 2 of 3 

1. Fill in the missing numbers. Some will require converting scientific notation to standard form, 

while others will require converting standard form to scientific notation. 

a. 6.03 × 10 –2 

b. 9.11 × 10 5 

c. 5.570 × 10 –7 

2. Explain why the numbers below are not written in scientific notation, then give the correct way to write the 

number in scientific notation. 

Example: 0.06 × 10 5 is not written in scientific notation because the first factor (0.06) is not greater than or 

equal to 1. The correct way to write this number in scientific notation is 6.0×10 3 . 

a. 2.004 × 1 11 

b. 56 × 10 –4 

c. 2 × 100 2 

d. 10 × 10 –6 


d. 999.0 

e. 264,000 

f. 761,000,000 

g. 7.13 × 10 7 

h. 0.00320 

i. 0.000040 

j. 1.2 × 10 –12 

k. 42,000,000,000,000 

l. 12,004,000,000 

m. 9.906 × 10 –2 

28.1

Page 3 of 3 

3. Write the numbers in the following statements in scientific notation: 

a. The national debt in 2005 was about $7,935,000,000,000. 

b. In 2005, the U.S. population was about 297,000,000 

c. Earth's crust contains approximately 120 trillion (120,000,000,000,000) metric tons of gold. 

d. The mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 91 kilograms. 

e. The usual growth of hair is 0.00033 meters per day. 

f. The population of Iraq in 2005 was approximately 26,000,000. 

g. The population of California in 2005 was approximately 33,900,000. 

h. The approximate area of California is 164,000 square miles. 

i. The approximate area of Iraq in 2005 was 169,000 square miles. 

j. In 2005, one right-fielder made a salary of $12,500,000 playing professional baseball. 

28.1

Name: Date: 

28.1 Understanding Light Years 

28.1 

How far is it from Los Angeles to New York? Pretty far, but it can still be measured in miles or 

kilometers. How far is it from Earth to the Sun? It’s about one hundred forty-nine million, six hundred thousand 

kilometers (149,600,000, or 1.496 × 10 8 km). Because this number is so large, and many other distances in space 

are even larger, scientists developed bigger units in order to measure them. An Astronomical Unit (AU) is 

1.496 × 10 8 km (the distance from Earth to the sun). This unit is usually used to measure distances within our 

solar system. To measure longer distances (like the distance between Earth and stars and other galaxies), the light 

year (ly) is used. A light year is the distance that light travels through space in one year, or 9.468 × 10 12 km. 

1. Converting light years (ly) to kilometers (km) 

Earth’s closest star (Proxima Centauri) is about 4.22 light years away. How far is this in kilometers? 

Explanation/Answer: Multiply the number of kilometers in one light year (9.468 × 10 12 km/ly) by the 

number of light years given (in this case, 4.22 ly). 

2. Converting kilometers to light years 

Polaris (the North Star) is about 4.07124 × 10 15 km from the earth. How far is this in light years? 

Explanation/Answer: Divide the number of kilometers (in this case, 4.07124 × 10 15 km) by the number of 

kilometers in one light year (9.468 × 10 12 km/ly). 

Convert each number of light years to kilometers. 

1. 6 light years 

2. 4.5 × 10 6 light years 

3. 4 × 10 –fio3 light years 

Convert each number of kilometers to light years. 

4. 5.06 × 10 16 km 

5. 11 km 

4.07124 10 15 × km 

6. 11,003,000,000,000 km 

9.468 10 12 

( 

-------------------------------------------- 

× ) km 

× 4.22 ly 3.995 10 

1 ly 

13 ≈ × km 

9.468 10 12 × km 4.07124 10 

÷ --------------------------------------- 

1 ly 

15 × km 1 ly 

--------------------------------------------- 

1 9.468 10 12 = × --------------------------------------- ≈ 

430 light years 

× km

Page 2 of 2 


7. The second brightest star in the sky (after Sirius) is Canopus. This yellow-white supergiant is about 

1.13616 × 10 16 kilometers away. How far away is it in light years? 

8. Regulus (one of the stars in the constellation Leo the Lion) is about 350 times brighter than the sun. It is 85 

light years away from the earth. How far is this in kilometers? 

9. The distance from earth to Pluto is about 28.61 AU from the earth. Remember that an AU = 1.496 × 108 km. 

How many kilometers is it from Pluto to the earth? 

10. If you were to travel in a straight line from Los Angeles to New York City, you would travel 3,940 

kilometers. How far is this in AU’s? 

11. Challenge: How many AU’s are equivalent to one light year? 

28.1

Name: Date: 

28.1 Parsecs 

You have already learned about two units of measurement commonly used in astronomy: 

• The astronomical unit (AU), which is the average distance between Earth and the Sun: 1.46 × 108 km 

• The light year (ly), which is the distance light travels through space in one year: 9.468 × 1012 km 

Chapter 28 of your text introduces a third unit of distance, the parsec (pc). The word parsec stands for “parallax 

of one arcsecond” which refers to the geometric method used by astronomers to figure out distances between 

objects in space. For our purposes, we will define the parsec as equal to 3.26 light years, or 206,265 astronomical 

units. This means that you would have to make 206,265 trips from Earth to the Sun (or 103,132.5 round trips) in 

order to travel 1 parsec! 

1 parsec = 3.26 light years or 206,265 astronomical units 

In this skill sheet, you will practice converting between parsecs, light years, astronomical units, and kilometers. 

1. Converting light years (ly) to parsecs (pc) 

Earth’s closest star (Proxima Centauri) is about 4.22 light years away. How far is this in parsecs? 

Explanation/Answer: Divide the number of light years given (in this case, 4.22 ly) by the number of light 

years in one parsec (3.26 ly). 

3.26 ly 1 pc 

4.22 ly ÷ = 4.22 ly× = 1.29 ly 

1 pc 3.26 ly 

2. Converting astronomical units (AU) to parsecs (pc) 

Polaris (the North Star) is about 2.789 × 107 astronomical units from Earth. How far is this in parsecs? 

Explanation/Answer: Divide the number of astronomical units (in this case, 2.789 × 10 7 AU) by the 

number of astronomical units in one parsec (206,265 AU). 

7 206,265 AU 7 1 pc 

2 

2.789× 10 AU ÷ = 2.789× 10 AU × = 1.352× 10 or 135.2 pc 

5 

1 pc 2.06265× 10 AU 

28.1

Page 2 of 2 

Convert each number of light years to parsecs. 

1. 6.00 light years 

2. 4.50 × 10 6 light years 

3. 4.00 × 10 -3 light years 

Convert each number of astronomical units to parsecs. 

4. 5.25 × 10 6 AU 

5. 100. AU 

6. 11,300,000 AU 


7. The Milky Way galaxy is about 100,000 light years across. How large is this in parsecs? 

8. The Andromeda galaxy is approximately 2,500,000 light years from Earth. How far is this in parsecs? 

9. Regulus (one of the stars in the constellation Leo the Lion) is about 85 light years from Earth. How far is this 

in parsecs? 

10. The average distance from the Sun to Pluto is approximately 29.6 astronomical units. How far is this in 

parsecs? 

28.1

Page 1 of 2 

28.1 Edwin Hubble 

Edwin Hubble was an accomplished academic that many astronomers credit with 

“discovering the universe.” 

A good student and even better athlete 

Edwin Hubble was born on 

November 29, 1889, in 

Marshfield, Missouri. His 

family moved to Chicago 

when he was ten years old. 

Hubble was an active, 

imaginative boy. He was an 

avid reader of science 

fiction. Jules Verne’s 

adventure novels were 

among his favorite stories. 

Science fascinated Hubble, and he loved the way 

Verne wove futuristic inventions and scientific 

content into stories that took the reader on voyages to 

some strange and exotic destinations. 

Hubble was a very good student and also an excellent 

athlete. In 1906 he set an Illinois state record for the 

high jump, and in that same season he took seven first 

place medals and one third place medal in a single 

high school track meet. 

Focus turns to academics 

Hubble continued his athletic success by participating 

in basketball and boxing at the University of Chicago. 

Eventually though, his studies became his primary 

focus. Hubble graduated with a bachelors degree in 

Mathematics and Astronomy in 1910. 

Hubble was selected as a Rhodes Scholar and spent 

the next three years at the University of Oxford, in 

England. Instead of continuing his studies in math and 

science, he decided to pursue a law degree. He 

completed the degree in 1913 and returned to the 

United States. He set up a law practice in Louisville, 

Kentucky. However, it was a short lived law career. 

Returning to Astronomy 

It took Hubble less than a year to become bored with 

his law practice, and he returned to the University of 

Chicago to study astronomy. He did much of his work 

at the Yerkes Observatory, and received his Ph.D. in 

astronomy in 1917. 

Hubble joined the army at this time and served a tour 

of duty in World War I. He attained the rank of Major. 

When he returned in 1919, he was offered a job by 

George Ellery Hale, the founder and director of 

Carnegie Institution's Mount Wilson Observatory, 

near Pasadena, California. 

28.1 

The best tool for the job 

The timing could not have been better. The 100-inch 

Hooker telescope, the world’s most powerful 

telescope at the time, had just been constructed. This 

telescope could easily focus images that were fuzzy, 

too dim, or too small to be seen clearly through other 

large telescopes. 

The Hooker telescope enabled Hubble to make some 

astounding discoveries. Astronomers had believed that 

the many large fuzzy patches they saw through their 

powerful telescopes were huge gas clouds within our 

own Milky Way galaxy. They called these fuzzy 

patches “nebulae,” a Greek word meaning “cloud.” 

Hubble’s observations in 1923 and 1924 proved that 

while a few of these fuzzy objects were inside our 

galaxy, most were in fact entire galaxies themselves, 

not only separate from the Milky Way but millions of 

light years away. This greatly enlarged the accepted 

size of the universe, which many scientists at the time 

believed was limited to the Milky Way alone. 

Another landmark discovery 

Hubble also used spectroscopy to study galaxies. He 

observed that galaxies’ spectral lines were shifting 

toward the red end of the spectrum, which meant they 

were moving away from each other. He showed that 

the farther away a galaxy was, the faster it was moving 

away from Earth. In 1929, Hubble and fellow 

astronomer Milton Humason announced that all 

observed galaxies are moving away from each other 

with a speed proportional to the distance between 

them. This became known as Hubble’s Law, and it 

proved that the universe was expanding. 

Albert Einstein visited Hubble and personally thanked 

him for this discovery, as it matched with Einstein’s 

calculations, providing observable evidence 

confirming his predictions. 

Hubble worked at the Wilson Observatory until his death 

in 1953. He is considered the father of modern 

cosmology. To honor him, scientists have named a space 

telescope, a crater on the moon, and an asteroid after him.

Page 2 of 2 


1. Look up the definition of each boldface word in the article. Write down the definitions and be sure 

to credit your source. 

2. Research: What is a Rhodes Scholarship? 

3. Research: Why does a larger telescope allow astronomers to see more? 

4. Imagine you knew Edwin Hubble. Describe how you think he may have felt when Albert Einstein came to 

visit and thank him for his discoveries. 

5. Research: Before Hubble’s discovery, people thought that the universe had always been about the same 

size. How did Hubble’s discovery that the universe is currently expanding change scientific thought about 

the size of the universe in the past? 

28.1

Name: Date: 

28.2 Light Intensity Problems 

Light is a form of energy. Light intensity describes the amount of energy per second falling on a surface, using 

units of watts per meter squared (W/m 2 ). Light intensity follows an inverse square law. This means that the 

intensity decreases as the square of the distance from the source. For example, if you double the distance from 

the source, the light intensity is one-fourth its original value. If you triple the distance, the light intensity is oneninth 

its original value. 

Most light sources distribute their light equally in all directions, 

producing a spherical pattern.The area of a sphere is 4πr 2 , where r is the 

radius or the distance from the light source. For a light source, the 

intensity is the power per area. The light intensity equation is: 

I 

= -- 

P 

= 

A 

P 

4πr 2 

----------- 

Remember that the power in this equation is the amount of light emitted 

by the light source. When you think of a “100 watt” light bulb, the 

number of watts represents how much energy the light bulb uses, not how much light it emits. Most of the energy 

in an incandescent light bulb is emitted as heat, not light. That 100-watt light bulb may emit less than 1 watt of 

light energy with the rest being lost as heat. 

Solve the following problems using the intensity equation. The first problem is done for you. 

1. For a light source of 60 watts, what is the intensity of light 1 meter away from the source? 

P P 

I = = 2 A 4πr 60 W 

2 

= = 

4.8 W/m 

2 

4 π(1m) 

2. For a light source of 60 watts, what is the intensity of light 10 meters away from the source? 

3. For a light source of 60 watts, what is the intensity of light 20 meters away from the source? 

4. If the distance from a light source doubles, how does light intensity change? 

5. Answer the following problems for a distance of 4 meters from the different light sources. 

a. What is the intensity of light 4 meters away from a 1-watt light source? 

b. What is the intensity of light 4 meters away from a 10-watt light source? 

c. What is the intensity of light 4 meters away from a 100-watt light source? 

d. What is the intensity of light 4 meters away from a 1,000-watt light source? 

6. What is the relationship between the watts of a light source and light intensity? 

28.2

Page 1 of 2 

28.2 Henrietta Leavitt 

Leavitt, although deaf, had a keen eye for observing the stars. Her ability to identify the magnitude 

of stars set the standard for determining a star's distance—hundreds or even millions of light years away. 

Star struck 

Henrietta Swan Leavitt was 

born on July 4, 1868 in 

Lancaster, Massachusetts. 

Henrietta's family lived in 

Cambridge, Massachusetts 

and later moved to 

Cleveland, Ohio. In Ohio, 

Leavitt attended Oberlin 

College for two years and 

was enrolled in the school's 

conservatory of music. She 

then moved back to 

Cambridge and attended Radcliffe College, which was 

then known as the Society for the Collegiate 

Instruction of Women. 

In her last year of college, Henrietta took an 

astronomy course—then began her fascination with 

and love for the stars. She graduated in 1892 and later 

became a volunteer research assistant working at the 

Harvard College Observatory. 

Computing the stars 

In the 1880s, Harvard College established a goal to 

catalog the stars. Edward Pickering, a former 

professor at the Massachusetts Institute of 

Technology, became director of the Harvard 

Observatory. Pickering was an authority in 

photographic photometry—determining a star's 

magnitude from a photograph. He wanted to gather 

information about the brightness and color of stars. 

In order to complete this work, Pickering needed 

people to perform the tedious task of examining 

photographs of stars. Men typically did not perform 

this type of work, but women were hired and known as 

“computers.” Leavitt was hired at a rate of $.30 per 

hour to complete this painstakingly detailed work. 

Leavitt was not a healthy woman, struggling with 

complete hearing loss and other illnesses during 

college and throughout her career. Despite these 

setbacks, she became a super computer, devoting her 

life to studying the stars. She eventually became the 

head of the photographic stellar photometry 

department. 

28.2 

Leavitt catalogued variable stars that altered in 

brightness over the course of a few days, weeks, or 

even months. She studied Cepheid variable stars in the 

Magellanic Clouds, two galaxies near the Milky Way. 

Leavitt examined photographic plates, comparing the 

same regions on several plates taken at different times. 

Stars that had changed in brightness would look 

different in size. Leavitt continued to examine plates, 

discovering nearly 2,000 new variable stars in the 

Magellenic Clouds. 

Leavitt found an inverse relationship between a star's 

brightness cycle and its magnitude. A stronger star 

took longer to cycle between brightness and dimness. 

Therefore, brighter Cepheid stars took longer to rotate 

between brightness and dimness. In 1912, Leavitt had 

established the Period-Luminosity relation. 

These stars, all located within the Magellenic Clouds, 

were roughly the same distance from the Earth. This 

rule provided astronomers with the ability to measure 

distances within and beyond our galaxy. 

Astronomical findings 

Leavitt's discovery had a tremendous impact on future 

research in the field of astronomy. Astronomers could 

now determine distances to galaxies and within the 

universe overall. Ejnar Hertzsprung was able to plot 

the distance of Cepheid stars. Harlow Shapley, using 

Leavitt's findings, was able to map the Milky Way and 

determine its size. Edwin Hubble applied her rule to 

establish the age of the Universe. 

An unsung heroine 

In 1925, the Swedish Academy of Sciences wished to 

nominate Leavitt for a Nobel Prize. However, she had 

died of cancer nearly four years earlier at the age of 

53. The Nobel Prize must be given during a recipient’s 

lifetime. 

In addition to her discovery of numerous variable 

stars, Leavitt discovered four novas and developed the 

standard method for determining the magnitude of 

stars. An asteroid and crater on the moon are named in 

her honor.

Page 2 of 2 


1. How did Henrietta Leavitt discover new variable stars? 

2. What were Leavitt's two significant contributions to the field of astronomy? 

3. Research: What is the name of the asteroid named in Leavitt's honor? 

4. Research: When was the Harvard Observatory established and what does It do now? 

5. Research: State three facts about each of these astronomers: Ejnar Hertzsprung, Harlow Shapley, and Edwin 

Hubble. 

6. Research: What is the Nobel Prize? 

28.2

Name: Date: 

28.2 Calculating Luminosity 

You have learned that in order to understand stars, astronomers want to know their luminosity. Luminosity 

describes how much light is coming from the star each second. Luminosity can be measured in watts (W). 

Measuring the luminosity of something as far away as a star is difficult to do. However, we can measure its 

brightness. Brightness describes the amount of the star’s light that reaches a square meter of Earth each second. 

Brightness is measured in watts/square meter (W/m 2 ). 

The brightness of a star depends on its luminosity and its distance from Earth. A star, like a light bulb, radiates 

light in all directions. Imagine that you are standing one meter away from an ordinary 100-watt incandescent 

light bulb. These light bulbs are about ten percent efficient. That means only ten percent of the 100 watts of 

electrical power is used to produce light. The rest is wasted as heat. So the luminosity of the bulb is about ten 

percent of 100 watts, or around 10 watts. 

The brightness of this bulb is the same at all points one meter away from the bulb. All those points together form 

a sphere with a radius of one meter, surrounding the bulb. 

If you want to find the brightness of that bulb, you take the luminosity (10 watts) and divide it by the amount of 

surface area it has to cover—the surface area of the sphere. So, the formula for brightness is: 

brightness 

The brightness of the bulb at a distance of one meter is: 

10 watts 

4π(1 meter) 2 

------------------------------ 

--------------------------------------------------luminosityluminosity 

surface area of sphere 

4π( radius) 

2 

= 

= ---------------------------- 

10 watts 

12.6 meter 2 

--------------------------- 0.79 W/m 2 

= 

= 

Notice that the radius in the equation is the same as the distance from the bulb to the point at which we’re 

measuring brightness. If you were standing 10 meters away from the bulb, you would use 10 for the radius in the 

equation. The surface area of your sphere would be 4π(100) or 1, 256 square meters! The same 10 watts of light 

energy is now spread over a much larger surface. Each square meter receives just 0.008 watts of light energy. Can 

you see why distance has such a huge impact on brightness? 

28.2

Page 2 of 2 

If we know the brightness and the distance, we can calculate luminosity by rearranging the equation: 

luminosity brightness × surface area of sphere brightness 4π(distance) 2 

= 

= × 

This is the same formula that astronomers use to calculate the luminosity of stars. 

You are standing 5 meters away from another incandescent light bulb. Using a light-meter, you measure its 

brightness at that distance to be 0.019 watts/meter 2 . Calculate the luminosity of the bulb. Assuming this bulb is 

also about ten percent efficient, estimate how much electric power it uses (this is the wattage printed on the bulb). 

Step 1: Plug the known values into the formula: 

0.019 watts 

luminosity 

meter 2 

-------------------------- 

4π( 5 meters) 

2 

= 

× ---------------------------------- 

1 

Step 2: Solve for luminosity: 

Step 3: If the bulb is only about ten percent efficient, the electric power used must be about ten times the 

luminosity. The bulb must use about 10 × 6 watts, or 60 watts, of electric power. 

1. Ten meters away from a flood lamp, you measure its brightness to be 0.024 W/m 2 . What is the luminosity of 

the flood lamp? What is the electrical power rating listed on the bulb, assuming it is ten percent efficient? 

2. You hold your light-meter a distance of one meter from the light bulb in your refrigerator. You measure the 

brightness to be 0.079 W/m 2 . What is the luminosity of this light bulb? What is its power rating, assuming it 

is ten percent efficient? 

3. Challenge: Finding the luminosity of the sun. 

You can use the same formula to calculate the luminosity of the sun. 

Astronomers have measured the average brightness of the sun at the top of Earth’s atmosphere to be 1,370 W/m 2 . 

This quantity is known as the solar constant. 

We also know that the distance from Earth to the sun is 150 billion meters (or 1.5 × 10 11 meters). 

What is the luminosity of the sun? 

luminosity = 

0.019 × 100π 

watts= 6 watts 

Hints: 

1. You may wish to rewrite the solar constant as 1.370 × 103 W/m2 . 

2. (10 11 ) 2 is the same as 1011 × 1011 . To find the product, add the exponents. 

3. Don’t forget to find the square of 1.5! 

28.2

Name: Date: 

28.3 Doppler Shift 

Doppler shift is an important tool used by astronomers to study the motion of objects, such as stars and galaxies, 

in space. For example, if an object is moving toward Earth, the light waves it emits are compressed, shifting them 

toward the blue end (shorter wavelengths, higher frequencies) of the visible spectrum. If an object is moving 

away from Earth, the light waves it emits are stretched, shifting them toward the red end (longer wavelengths, 

lower frequencies) of the visible spectrum. In this skill sheet, you will practice solving problems that involve 

doppler shift. 

Understanding Doppler Shift 

28.3 

You have learned that astronomers use a spectrometer to determine which 

elements are found in stars and other objects in space. When burned, each 

element on the periodic table produces a characteristic set of spectral lines. 

When an object in space is moving very fast, its spectral lines show the 

characteristic patterns for the elements it contains. However, these lines 

are shifted. 

If the object is moving away from Earth, its spectral lines are shifted 

toward the red end of the spectrum. If the object is moving toward Earth, 

its spectral lines are shifted toward the blue end of the spectrum. 

1. The graphic to the right shows two spectral lines from an object that is not 

moving. Use an arrow to indicate the direction that the spectrum would appear to 

shift if the object was moving toward you. 

2. The graphic to the right shows the spectral 

lines emitted by four moving objects. The 

spectral lines for when the object is 

stationary are shown as dotted lines on each 

spectrum. The faster a star is moving, the 

greater the shift in wavelength. Use the 

graphic to help you answer the following 

questions. 

a. Which of the spectra show an object 

that is moving toward you? 

b. Which of the spectra show an object 

that is moving away from you? 

c. Which of the spectra show an object that is moving the fastest away from you? 

d. Which of the spectra show an object that is moving the fastest toward you?

Page 2 of 2 

Solving Doppler Shift Problems 

28.3 

By analyzing the shift in wavelength, you can also determine the speed at which a star is moving. The 

faster a star is moving, the larger the shift in wavelength. The following proportion is used to help you calculate 

the speed of a moving star. Remember that the speed of light is a constant value equal to 3 × 10 8 m/s. 

The 

-------------------------------------------speed 

of a star 

The speed of light 

= 

------------------------------------------------------------------------------------- 

The difference in wavelength 

The stationary value for wavelength 

The spectral lines emitted by a distant galaxy are analyzed. One of the lines for hydrogen has shifted from 450 

nm to 498 nm. Is this galaxy moving away from or toward Earth? What is the speed of galaxy? 

The speed of a star 

3 10 8 -------------------------------------------- 

× m/s 

= 

498 nm – 450 nm 

----------------------------------------- 

450 nm 

The speed of a star 

48 nm 

----------------- 3 10 

450 nm 

8 × × m/s 0.11 3 10 8 × × m/s 3.3 10 7 = = = 

× m/s 

The galaxy is moving away from Earth at a speed of 33 million meters per second. 

1. One of the spectral lines for a star has shifted from 535 nm to 545 nm. What is the speed of this star? Is the 

star moving away from or toward Earth? 

2. One of the spectral lines for a star has shifted from 560 nm to 544 nm. What is the speed of the star? Is it 

moving away from or toward Earth? 

3. An astronomer has determined that two galaxies are moving away from Earth. A spectral line for galaxy A is 

red shifted from 501 nm to 510 nm. The same line for galaxy B is red shifted from 525 nm to 540 nm. Which 

galaxy is moving the fastest? Justify your answer. 

4. Does the fact that both galaxies in the question above are moving away from Earth support or refute the Big 

Bang theory? Explain your answer.

Answer Keys 

Skill Sheet 1.1: Lab Safety 

Safety quiz answers: 

1. Answers will vary. 


3. Answers will vary. Example: (1) Be quite and listen, (2) 

Locate your safety buddy, (3) In a safe and orderly manner, 

follow your teacher out of the lab to a designated safe 

location. 

4. In many cases, investigations require the use of chemicals 

that may cause harm to your eyes or clothing if these are not 

protected. Gloves are also important when working with 

chemicals. For investigations that require heat, using a hot 

pad is very important. 

5. Teamwork helps you to complete the lab efficiently, but 

keeping safe also requires teamwork. Sometimes, you may 

need someone to help you pour a chemical or perform a 

procedure that would be unsafe if you tried it by yourself. A 

team of people can also work together to keep everyone on 

the team safe. On your own, it is more difficult to be aware of 

all the possible dangers in a laboratory setting. 

6. Cleaning up after an investigation prepares the work space for 

the next day’s investigation. A clean work space is safer 

because all chemicals and any sharp or dangerous objects are 

removed. Clean up also involves turning off any appliances 

that could heat up and cause a fire. 

7. (1) Immediately tell my teacher, (2) Listen carefully and 

follow any safety instructions provided by the teacher, and (3) 

Follow the appropriate safety guidelines. 

8. Answers are: 

a. First, I would make sure that my classmates know to stay 

away from the broken beaker and I would tell my teacher 

what had happened. Then, I would clean up the glass with 

Skill Sheet 1.1: Using Your Textbook 

Part 1 answers: 

1. Green 

2. Correct answers include any four of the following vocabulary 

words: 

relief, elevation, sea level, topographic map, contour lines, 

slope 

3. blue 

4. Hypotheses must be testable to be scientific. 

5. Section reviews are found at the end of each section of each 

chapter. 

6. Why does chocolate melt in your hand? 


1. Looking for: 

2. Given 

3. Relationships 

4. Solution 

8. The four parts are vocabulary, concepts, problems, and 

applying your knowledge. 

Skill Sheet 1.1: SI Units 

1. 10 g 

2. 1000 mm 

3. 600 mm 

4. 420 g 

5. 5 L 

6. 0.1 m 

Page 1 of 57 

a dust pan and a brush. I would not use my hands to clean 

up the glass. I would place the broken glass in a cardboard 

box, seal the box, and label it “sharps.” 

b. I would make sure my classmates know about the water so 

they don’t slip. I would tell my teacher as soon as 

possible. I would begin placing paper towels on the wet 

spot as soon as possible. Carefully, I would work with my 

classmates to clean up the spill. It would be best to use 

gloves during the clean up in case any chemicals are 

mixed in with the water. 

c. I would tell my teacher about the smell and follow any 

safety instructions given to me by the teacher. I would 

help to make sure that the lab is well ventilated (by 

helping to open windows and doors, for example). I would 

ask to leave the lab to get some fresh air if I needed to do 

so. 

d. I would stop talking and listen to any safety instructions 

from my teacher. I would follow the classroom plan for 

exiting the lab as soon as possible. I would not worry 

about removing my lab apron. I may remove my goggles 

if it seems unsafe to keep them on. 

e. I would take her hand and lead her to the eye wash station 

as soon as possible. I would tell a classmate to tell our 

teacher as soon as possible. When the teacher arrives, I 

would let her/him help my lab partner. 

f. I would stop talking and listen to any safety instructions 

from my teacher. I would follow the classroom plan for 

exiting the lab as soon as possible. I may need to use the 

nearest classroom fire extinguisher if my teacher is unable 

to do so. 


1. There are eight units: 

Science Skills 

Motion, Force, and Energy 

Matter, Energy, and Earth 

Matter and Its Changes 

Electricity and Magnetism 

Earth’s Structure 

Waves 

Matter and Motion in the Universe 

2. Answers will vary according to student interest. 

3. The glossary and index are found at the back of the book, 

after Unit 8. The glossary contains definitions; the index tells 

where to find information on specific topics. 


1. Velocity is a variable that tells you both speed and direction. 

2. Pages 250 and 251 

3. Page 347 

7. 1,500,000 mg 

8. 300 L 

9. 6,500,000 cm 

10. 120,000 mg 

11. 7.2 L 

12. 5.3 kL

13. A decimeter is 100 times larger than a millimeter. 

14. A dekagram is 1000 times larger than a centigram 

Skill Sheet 1.1: Scientific Notation 


a. 122,200 

b. 90,100,000 

c. 3,600 

d. 700.3 

e. 52,722 

Skill Sheet 1.2: Measuring Length 

Stop and Think: 

f. 10 millimeters = 1 centimeter 

g. It is better to measure with the English system when you 

want to buy fabric for making curtains. Fabric is sold in 

yards and inches in the U.S. It is better to measure with 

the metric system when you are describing the length of 

something to your pen pal in Germany. 

Example 1: 

1. 63.0 mm 

2. 6.30 cm 

3. 0.063 m 

Example 2: 

1. 189.0 mm 

2. 3 blocks 

3. 7.44 inches 

Example 3: 

1. 42.5 mm 

2. 7 dominoes 

Skill Sheet 1.2: Averaging 

1. Four gloves per household 

2. On average, each person spent about $8.33. 

3. $3.95; $31.60 

Skill Sheet 1.2: SQ3R Reading and Study Method 

No student responses are required. 

Skill Sheet 1.2: Stopwatch Math 


a. 5, 5.05, 5.15, 5.2, 5.5 

b. 6:06, 6:06.004, 6:06.04, 6:06.4 


Time 9.88w 9.88w 9.91 9.95w 

Year 2002 1998 2004 2001 

Time 9.97w 10.01 10.08 10.11 

Year 1999 2000 2005 2003 

Skill Sheet 1.2: Understanding Light Years 

1. 5.7 × 10 13 km 

2. 4.3 × 10 19 km 

3. 3.8 × 10 10 km 

4. 5,344 ly 

5. 1.16 × 10 –12 ly 

6. 1.16 ly 

Page 2 of 57 

15. A millimeter is 10 times smaller than a centimeter. 


a. 4.051 × 10 6 

b. 1.3 × 10 9 

c. 1.003 × 10 6 

d. 1.602 × 10 4 

e. 9.9999 × 10 12 

Practice with converting units for length: 

Prefix Your multiplication factor Your domino length in: 

pico- 10 -9 

42.5 × 10 9 pm 

nano- 10 -6 42.5 × 10 6 nm 

micro- 10-3 42.5 × 103 µm 

milli 10 0 

42.5 × 10 0 mm 

centi- 10 1 42.5 × 10 –1 cm 

deci- 10242.5 × 10 –2 dm 

deka- 10 4 

42.5 × 10 –4 dam 

hecto- 10 5 42.5 × 10 –5 hm 

kilo- 10 6 42.5 × 10 –6 km 

4. ≈ 6 points each 

5. ≈ 5 slices each (5 1 / 3 slices each) 


a. 1:22.04, 1:22.4, 1:23.117, 1:23.2, 1:24, 1:24.007, 1:25, 

1:33 

b. 1:17.99, 1:18.22, 1:18.3, 1:20, 1:20.22, 1:21.003, 1:21.2 

c. 1:24.099, 1:24.9899, 1:24.99, 1:24.9901, 1:25, 1:25.001 

4. Infinitely many solutions possible. 

Example: 26:15.21, 26:15.215, 26:15.22, 26:15.225, 26:15.23 

7. 1,200 ly 

8. 8.0478 × 10 14 km 

9. 4,280,056,000 km, or 4.28 × 10 9 km 

10. 0.000026336 AU, or 2.6 × 10 –5 AU 

11. 63,288 AU

Skill Sheet 1.2: Indirect Measurement 

1. The tree is 3 meters tall. 

2. The flagpole’s shadow is 12.8 meters. 


a. 2,200 feet 

b. 670 meters 

4. The average mass is 0.1 kilogram or 100 grams. 

5. Each staple is 0.0324 gram or 3.24 milligrams. 

6. One business card is 0.034 centimeter thick. 

7. The thickness of a CD is approximately 0.13 centimeter or 

1.3 millimeters. 


a. 4.8 millimeters 

b. 9.6 millimeters 

c. 48 millimeters 

d. 9,600 millimeters or 9.6 meters 


a. Each cheesecake takes 0.85 hour or 51 minutes to make. 

b. Yvonne earns $12 per cheesecake. 

c. Yvonne earns $14.12 per hour. 

Skill Sheet 1.3: Dimensional Analysis 


a. $72/day 

b. 210 lbs/week 


a. 2.75 gal 

b. 2.20 m 

c. ≈ 0.0947 mile 

d. 64 cups 

Skill Sheet 1.3: Fractions Review 


1. 13 / 12 

2. 89 / 56 

3. 19 / 6 

4. 1.1, 1.6, 3.2 


1. –5 / 12 

2. 9 / 56 

3. –5 / 3 

4. –0.42, 0.16, –1.67 


1. 1 / 4 

2. 5 / 8 

Page 3 of 57 

10. The mass of the block of marble is 324,000 grams or 

324 kilograms. 

11. Sample answer: 

First fill the dropper with water from the glass. 

Then place drops of water one-by-one into the graduated 

cylinder. Count the number of drops it takes to reach the 

5.0 mL mark on the graduated cylinder. 

To find the volume of one drop, divide the value 5.0 mL by 

the number of drops. 

12. Sample answer: 

(1) Remove the newspaper from the recycling bin. 

(2) Unfold each sheet and smooth the paper. 

(3) Neatly stack the sheets of paper. 

(4) Place the newspaper on a flat surface. 

(5) Place something heavy, like a hardbound book, on the 

newspaper to remove excess space between the sheets of paper. 

(6) Measure the height of the stack of newspaper. 

(7) Divide the stack of paper by the number of sheets. 

Note to teacher: This question is designed to prompt students to 

think about sources of experimental error. You may wish to ask 

the students what would happen if they divided the height of the 

recycle bin by the number of sheets of newsprint multiplied by 

four. Why wouldn’t this method yield an accurate result? 


a. 126,144,000 s 

b. ≈ 71.0 ft 

c. 4.5 qt 

d. 14 2 / 3 fields 

e. 48. km/gal 

f. ≈ 13 km/l 

g. 95 ft/s 

3. 15 / 16 

4. 0.25, 0.63, 0.94 


1. 4 / 9 

2. 49 / 40 

3. 2 

4. 2 / 3 

5. 0.44, 1.23, 2, 0.67 


1. 1 

2. 27 / 70 

3. 1 

4. 5 / 6 

5. 1, 0.39, 1, 0.83

Skill Sheet 1.3: Significant Digits 


a. 4 

b. 1 

c. 4 

d. 2 

e. 2 

f. 3 

g. infinitely many (# of students is counted) 

Skill Sheet 1.3: Study Notes 

This skill sheet provides a note-taking grid for students. It can be 

used with reading assignments throughout the school year. 

Skill Sheet 1.3: Science Vocabulary 

Prefix is in bold and suffix is underlined: 

thermometer electrolyte monoatomic 

volumetric endothermic spectroscope 

prototype convex supersaturated 

Student definitions: 

Answers may vary. Correct answers include: 

1. The study of water 

2. Many units 

3. The same kind 

4. Different kinds 

5. Existing light 

6. An instrument for measuring the full range of something 

Dictionary definitions: 

1. The science dealing with the properties, distribution, and 

circulation of water 

2. A chemical compound formed by the union of small 

molecules, usually consisting of repeating units 

3. Of the same kind, having uniform structure 

Skill Sheet 1.3: SI Units Extra Practice 

1. 12,756,000 m 

2. 347,600,000 cm 

3. 384,000 km 

4. 200,000,000 m 

5. 16,000,000 cm 

6. 3,600,000 mm 

7. 125,000 m long, 400 m deep, 1,500 m wide 

8. 11.18 km/sec 

9. 5,400,000 g 

10. 2 g 

Skill Sheet 1.3: SI-English Conversions 

1. ≈ 4.3 mi 

2. ≈ 4.11 oz 

3. ≈ 896 kg 

4. ≈ 2.1 qt 

5. ≈ 2,400 g 

6. ≈ 33 mi 

7. 2830 in; 78.7 yd 

8. ≈ 1.74 mi 

9. ≈ 3.77 L 

10. ≈ 0.379 lb 

Page 4 of 57 


1. 34,000 cm 2 

2. 0.9 liters 

3. 12.8 m 2 

4. 24.2°C 

5. 40:32 


4. Consisting of dissimilar ingredients 

5. The emission of light (as by a chemical or physiological 

process) 

6. An instrument for measuring spectra 

Definitions based on prefixes and suffixes: 

1. thermometer 

2. sonogram (or sonograph) 

3. monoatomic 

4. telescope 

Word Dictionary Definition 

thermometer An instrument for measuring temperature 

sonogram A graph that shows the loudness of sound at 

different frequencies 

monoatomic Containing only one type of atom 

telescope A cylindrical instrument for viewing distant 

objects 

11. 1,200 mg to 2,700 mg 

12. 158,000 kg 

13. 450,000,000 mg 

14. 23,000 g to 90,000 g 

15. 40,000 mL 

16. 1,000 mL 

17. 26,600 kL 

18. 1,558,000 L 

19. 60 mL 

20. 0.947 L

Skill Sheet 1.4: Creating Scatterplots 


Data pair 

not necessarily 

in order 

Temp. Hours of 

heating 

Stopping 

distance 

Number of 

people 

in family 

Stream 

flow 

Tree 

age 



Hours of 

heating 

Page 5 of 57 

a. Table answers: 

b. 60 minutes 

c. 27.0 kilometers 

d. Adjusted scale for the x-axis: 3 per line or 5 per line; 

adjusted scale for the y-axis: 1.5 per line or 2 per line 

e. & f. 

Graph of position (km) vs. time (min): 

Time (min) 

g. After 45 minutes, the position would be about 

25.25 kilometers. 

Skill Sheet 1.4: What’s the Scale? 

1. Answers are: 2. The range is 30 and the scale is 1 per line. 

Range 

from 0 

14 

# of 

Lines 

10 

Range ≥ # of Lines 

14 ≥ 10 = ≥ 

Calculated 

scale 

1.4 

Adj. scale 

(whole #) 

2 

3. The range is 25 and the scale is 3 per line. 


Independent variable: Days; Dependent variable: Average 

Temperature (°F) 

8 

1000 

5 

20 

8 ≥ 5 =≥ 

1000 ≥ 20 = ≥ 

1.6 

50 

2 

50 

Range for x-axis = 11; Range for y-axis = 73 

Scale for x-axis = 1 day/box; Scale for y-axis = 4 °F/box 

547 15 547 ≥ 15 = ≥ 36.5 37 

99 30 99 ≥ 30 = ≥ 3.3 4 

35 12 35 ≥ 12 = ≥ 2.9 3 

Skill Sheet 1.4: Interpreting Graphs 

Independent Dependent 

Temp. 

Speed of a car Speed of a car Stopping 

distance 

Cost 

per week 

for groceries 

Number of 

people 

in family 

Cost 

per week 

for groceries 

Rainfall Amount of rainfall Rate of 

stream flow 

Average tree 

height 

Test score Number of 

hours studying 

for a test 

Population of 

a city 

Range Number 

of lines 

Number of 

schools needed 

Tree age Average tree 

height 

Number of hours Test score 

studying 

Population of a city Number of 

schools needed 

Range ≥ No. 

of lines 

Calculated 

scale 

(per line) 

Adj. 

scale 

(per line) 

13 24 13 ≥ 24 0.54 1 

83 43 83 ≥ 43 1.9 2 

31 35 31 ≥ 35 0.88 1 

100 33 100 ≥ 33 3.03 5 

300 20 300 ≥ 20 15 15 

900 15 900 ≥ 15 60 60 

Practice set 1: Scatterplot 

1. Graph title: “Money in cash box vs. hours washing cars.” 

2. The two variables are number of hours washing cars and the 

amount of money in the cash box. 

3. Hours 

Independent variable Dependent variable 

0 5.0 

10 9.5 

20 14.0 

30 18.5 

40 23.0 

50 27.5 

60 32.0 

4. Dollars 

5. 0 to 6 

6. The data would be concentrated toward the bottom quarter of 

the graph. All the data would appear within first three grid 

boxes of the y-axis.

7. Yes, there is a relationship between the variables. 

8. As the time spent washing cars increases, the money in the 

cash box increases. 

9. If the theater club worked for five hours a Saturday for at least 

14 Saturdays, they could earn $1050. This amount is based on 

earning $75 during the five hour period (assuming $20 is the 

starting amount of money in the cash box). Between April 

and the fall, there would the Saturdays in May, June, July, and 

August for doing the car wash; a total of about 16 Saturdays. 

This would be enough time to earn $1000. 

Practice set 2: Bar Graph 

1. Graph title: “Percentage of teenagers that are employed in 

four cities.” 

2. The two variables represented on the x-axis are cities (four are 

represented) and gender (boys and girls). The variable 

represented on the y-axis is the percentage of teenagers that 

are employed. The range of values is from 0 to 80. 

3. The highest percentages of boys and girls employed is in city 

C. The lowest percentages is in city D. The percentages of 

boys and girls employed is about the same in city A which has 

the second highest percentage of teenagers employed. Girls 

employed outnumber boys employed in cities B and D. 

4. In cities A and C, the percentage of boys employed is greater 

than the percentage of girls employed. In cities B and D, the 

percentage of girls employed is greater than the percentage of 

boys employed. 

5. Answers will vary. Sample Answer: 

The type of businesses in city C are suited to hiring workers 

that can only work in the afternoons or evenings for a pay rate 

that is suitable to teenagers. The type of jobs in city D are 

more suited to people who can work full time. 

6. Answers will vary. Sample Answer: 

In city C, the kinds of jobs that are available to teenagers may 

be more suited for boys. The opposite is true for city B; there, 

the jobs may be more suitable and appealing to girls. By 

doing a survey of the teens in city C, this hypothesis could be 

tested. 

Practice set 3: Pie graph 

1. Graph title: “Percent distribution of jobs held by teenagers.” 

Skill Sheet 1.4: Recognizing Patterns on Graphs 

1. A, E, F 

2. B, C 

3. A, B, F 

Skill Sheet 2.1: Scientific Processes 

1. Maria and Elena’s question is: Does hot water in an ice cube 

tray freeze faster than cold water in an ice cube tray? 

2. Maria’s hypothesis: Hot water will take longer to freeze into 

solid ice cubes than cold water, because the hot water 

molecules have to slow down more than cold water molecules 

to enter the solid state and become ice. 

3. Examples of variables include: 

Amount of water in each ice cube tray “slot” must be 

uniform. 

Each ice cube tray must be made of same material, “slots” in 

all trays must be identical. 

Placement of trays in freezer must provide equal cooling. 

All “hot” water must be at the same initial temperature. 

All “cold” water must be at the same initial temperature. 

4. Examples of measurements include: 

Initial temperature of hot water. 

Initial temperature of cold water. 

Volume of water to fill each ice cube tray “slot.” 

Page 6 of 57 

2. Types of jobs held by teenagers and the percentages. 

3. No units are used in this graph. Instead, the graph is showing 

how categories (jobs in this case) are related to each other. 

4. The majority of jobs held by teenagers are in the retail 

industry (28%). Working teenagers are next likely to work in 

the food service industry (23%) and administrative support 

(21%). Other kinds of jobs held by teenagers include freight 

and stock handling (15%) and farm work (10%). Three 

percent of working teenagers participate in jobs that are not 

included in these categories. 

5. Answers will vary. A sample hypothesis based on this data is: 

The numbers of teenage girls and boys working in each job 

category is equal. I could test this hypothesis by interviewing 

employed teenagers that represent each job category. I would 

compare the numbers of girls and boys working in each 

category to see if my hypothesis is correct. 


Practice set 4: Line graph 

1. Graph title: “Springfield High School Population 1970-2005” 

2. The two variables are the year and the number of students. 

3. The range of x-axis values is the 35 years between 1970 and 

2005. The range of y-axis values is 900-1,400 students, a 

population difference of 500 students. 

4. The student population rose sharply between 1970 and 1980, 

from just over 1,000 students to almost 1,400 students. Then 

the population plummeted to about 1,000 students between 

1980 and 1985. 

5. a. Student answers will vary. Possible reasons include an 

economic decline in the district (perhaps a major industry 

closed), a government home buyout (this can happen in 

conjunction with a major airport expansion, for example), 

or the school district may have built a new high school to 

ease overcrowding. 

b. Student answers will vary. Students could call the district 

office, ask a school staff member who was there during 

that time period, or ask a friend or relative who lived in 

the district. 

6. This is a line graph, not a scatterplot, because the x-values 

have no cause-and-effect relationship with the y-values. 

4. C, E 

5. D 

6. A 

Time taken for water to freeze solid. 

5. Sample procedure in 9 steps: 

(1) Place 1 liter of water in a refrigerator to chill for 1 hour. 

(2) Boil water in pot on a stove (water will be 100°C). 

(3) Using pot holders, a kitchen funnel, and a medicinemeasuring 

cup, carefully measure out 15 mL of boiling water 

into each slot in two labeled ice cube trays. 

(4) Remove chilled water from refrigerator, measure 

temperature. 

(5) Carefully measure 15 mL chilled water into each slot in 

two labeled ice cube trays. 

(6) Place trays on bottom shelf of freezer, along the back wall. 

(7) Start timer. 

(8) After 1/2 hour, begin checking trays every 15 minutes to 

see if solid ice has formed in any tray. 

(9) Stop timing when at least one tray has solid ice cubes in it. 

6. The average time was 3 hours and 15 minutes.

7. Repeating experiments ensures the accuracy of your results. 

Each time you are able to repeat your results, you reduce the 

effect of sources of error in the experiment that may come 

from following a certain procedure, human error, or from the 

conditions in which the experiment is taking place. 

8. The only valid conclusion that can be drawn is (d). 

9. Maria and Elena could ask a few of their friends to repeat 

their experiment. This would mean that the experiment would 

be repeated in other places with other freezers. If their friends 

Skill Sheet 2.1: What’s Your Hypothesis? 

1. Sample hypothesis: The water level in the cup is lower 

because the Sun heated the water in the cup and that caused 

evaporation of the water. 

2. Sample hypothesis: The candle heats up the air above it. 

Warm air is less dense so it rises. The effect causes the air in 

the box to move in the area above the candle. When the 

smoke from moves above the candle, it gets heated and rises 

out of the chimney above the candle. 

3. Sample hypothesis: Increasing the temperature of water will 

increase the rate at which evaporation occurs. 

4. Sample hypothesis: If the river is flowing down a mountain, it 

will flow faster than if it is flowing along flat land. In other 

words, the force of gravity causes river water to flow faster if 

the water is moving from a high to a lower place. 

Skill Sheet 2.2: Recording Observations in the Lab 

Exercise 1: 

1. c 

2. a 

3. c 

Skill Sheet 2.2: Lab Report Format 

This skill sheet can be used throughout the school year as a guide 

to writing a formal lab report. 

Skill Sheet 2.2: Using Computer Spreadsheets 

Example graph: 

1. Time is the independent variable; temperature is the 

dependent variable. 

2. The independent variable goes in the first column. 

3. The temperature increases slowly for the first 90 seconds and 

then increases much more rapidly from 90-300 seconds. 

Page 7 of 57 

are able to repeat the girls’ results, then the kind of freezer 

used can be eliminated as a factor that influenced the results. 

10. A new question could be: Do dissolved minerals in water 

affect how fast water freezes? 

For further study: Ask student to come up with a plan to test 

the validity of statements b and c. Encourage your students to 

research methods for measuring dissolved minerals and 

oxygen in water. 

5. Sample hypothesis: I think the flower bulbs have been dug up 

and eaten by squirrels. 

6. Sample hypothesis: Since kelp is a food source for the sea 

urchins, the urchin population might die out. Without a sea 

urchin population as a food source, the sea otter population 

might die out. 

7. Sample hypothesis: Snowshoe hares turn white in the winter 

so that they can blend in with the snow and avoid being 

caught by lynx. In the summertime, the brown coat of the hare 

blends in with the color of the ground. 

8. Sample hypothesis: Yes, I think there would be animals like 

coyotes in other deserts. [Example: The jackal in the Kalahari 

Desert in Southwest Africa plays a similar ecological role as 

the coyote.] 

Exercise 2: 

a. Disappearance of copper color on pennies 

b. Mass by year 

c. Data/observations 

d. answers vary. 

4. The slope for the first 90 seconds is 0.02 degrees per second, 

and then it increases to 0.08 degrees per second for the period 

from 180 to 300 seconds. 

5.

6. 

The slope is the same (2.0) until you get to the final segment, 

when it increases to 2.6. 

Skill Sheet 2.2: Identifying Control and Experimental Variables 

1. Experimental variable: antibacterial cleaner (antibacterial 

cleaner vs. no antibacterial cleaner). Control Variables: Petri 

dish, cotton swab, source of bacteria, length of experiment, 

incubation temperature, incubation light exposure 

2. Experimental variable: amount of water each plant gets. 

Control variables: plant type, plant size, pot, soil, duration of 

experiment, amount of light exposure. 

Skill Sheet 3.1: Position on the Coordinate Plane 

1. 

2. 

Page 8 of 57 

3. Experimental variable: bread type (preservatives vs. no 

preservatives). Control variables: plastic bag, damp paper 

towel, dark environment, duration of experiment. 

4. Experimental variable: fertilizer (fertilizer vs. no fertilizer). 

Control variables: amount of water, algae sample, location of 

beakers (sunlight), duration of experiment. 

3. Yes the order does matter. The coordinate (2, 3) shows a point 

that is 2 to the right and 3 up, while the coordinate (3, 2) 

shows a point that is 3 to the right and 2 up.

Skill Sheet 3.1: Latitude and Longitude 



a. Iceland 

b. Algeria 

c. Argentina 

d. Australia 

e. New Zealand 


a. Bay of Bengal 

b. Aegean Sea 

c. Red Sea 

d. Gulf of Mexico 

Skill Sheet 3.1: Map Scales 


a. Andora 

b. No. I need to know the scale to answer the question. 

c. Yes. They are both 1.5 cm. 

d. No. One centimeter could represent different distances on 

each island. 

e. Calypso is much bigger. 


(Note: Allow answers that are + or – 3 kilometers.) 

a. 40 km 

Skill Sheet 3.1: Vectors on a Map 

1. (+60 km, –10 km) 

2. (+1 km, +2 km) 

3. (+1 km, +1 km) 

Skill Sheet 3.1: Navigation 

Note to teacher: It is highly recommended that you do a trial run 

yourself before doing this activity with your students. This 

will enable you to help the students more efficiently during 

the activity, especially when it comes to finding locations on 

the maps. 


a. I expect to find coral reefs. 

b. We will need to watch where we navigate our boat 

because coral reefs exist close to the surface and could be 

an obstruction for our boat. 

It’s time to go! 

1. No student response required. 


3. 1:326,856 

Page 9 of 57 

e. Baffin Bay 



a. 30.33°N 

b. 45.75°N 

c. 20.61°S 

d. 60.33°S 


a. 25.92°E 

b. 145.25°E 

c. 130.62°W 

d. 85.44°W 

b. 128 km 

c. 50 km 

d. 110 km 

e. 80 km 

f. 185 km 

g. 125 km 

h. 170 km (50 + 120) 

i. 118 km (78 + 40) 

j. 298 km (120 + 50 + 128) 

Bonus: Give credit for estimates between 850 – 950 km. 

4. 

5. Answers to student-designed problems will vary. 

4. It means that one unit on the map represents 326,856 of those 

units in real life. 

5. There are six feet in a fathom. 

6. There is a lighthouse with an occulting light, which means the 

period of darkness when the light is covered or obscured is 

less than the time period when the light is showing. 

7. Two fathoms 

8. Dump site of dredged material 

9. Dredged material is material that was dug by machine 

(usually from another channel or river bed) and has been 

dumped here. 

10. Yes 

11. No 

12. Yes

13. S Sh—Sand and shells on the bottom, Co Sh—coral shells on 

bottom, h S—hard sand on bottom, Co S—coral sand on 

bottom, bk SH—broken shells on bottom, bk Co—broken 

coral on bottom, Sh Co—shells and coral on bottom 

14. It is a flashing lighthouse. The light is obscured for longer 

than it is showing (the opposite is true with an occulting 

light). 


16. Explosive Dumping Area 

17. A bad idea! 

18. No. Lower the anchor and use the rowboat to get ashore. 

19. Four 

20. The fourth is aeronautical, which means that it displays 

flashes, in this case, of white and green, to indicate the 

location of an airport, a heliport, a landmark, a certain point 

of a federal airway in mountainous terrain, or an obstruction. 

21. Seven nautical miles 

22. Cables 

23. Drop anchor 

24. No 

25. It means that the rocks on the isle are covered and uncovered 

by water and that they reach a height of 269 feet. 

26. Fathoms 


28. 1:100,000 

29. You can see more detail on the second map. 

30. National Response Center or the nearest US Coast Guard 

facility 

Skill Sheet 3.2: Topographic Maps 

1. Answer graphic: 2. Answer graphic (at 

right): 


a. 0 or sea level 

b. 400-499 feet 

c. 100 feet 

d. 300 feet 

e. between 0 and 

100 feet. 


a. The island 

becomes two 

islands. 

Skill Sheet 3.3: Bathymetric Maps 

1. Example answers: 

a. Mid-Atlantic Ridge 

b. East Pacific Rise 

c. Middle America Trench or Mariana Trench 

d. Falkland Plateau 

e. Mendocino Fracture Zone 

2. Two tectonic plates move apart. 


a. East Pacific Rise 

b. Chile Rise; this rise looks like the Mid-Atlantic Ridge 

c. Chatham Rise; this feature seems to be a plateau on the sea 

floor 

4. Subduction 

Page 10 of 57 

31. WXM-96; 162.475 Hz 

32. 2.5 fathoms 

33. Going right up to the shore gives you three feet of water 

below the ship—that’s not very much. It is recommended to 

anchor further out and row or perhaps swim to shore. 

34. 46 feet 

35. Coral shells 

36. A cay is a small, low island or reef made mostly of sand or 

coral. 

37. Cables 

38. feet 

39. 1:15,000 

40. More detail is evident in this map than the other two. 

41. The lines represent areas that have been swept clear, called 

wire-dragged areas. The depth is noted on the map to 42 feet 

offshore of the solid line and to 36 feet between the solid and 

dashed lines. 

42. We know that our boat is clear in this area because our boat is 

12 feet deep. 

43. Yes 

44. Row in—it is a very shallow channel with many areas even 

less than five feet deep. 


46. Yes 





b. The original island is now three islands. 

c. No, the storm wave would wash over the island. 

5. A combination of two diverging plates at the East Pacific Rise 

and subduction zones in the northern part of the North Pacific 

Ocean. The plate movement associated with these features 

may have caused the fracture zone. 

6. The ridge has a lot of faults. There is a thin, dark-blue line in 

the middle of the ridge. The white areas around the ridge are 

not very prominent. 

7. This rise is less jagged. The white area near the rise is more 

prominent here than at the Mid-Atlantic Ridge. 

8. Mid-Atlantic Ridge; the dark line indicates a valley in the 

middle of the ridge 

9. Cross-sections of the Mid-Atlantic Ridge and the East Pacific 

Rise (Based on viewing the bathymetric map):

Mid-Atlantic Ridge cross-section East Pacific Rise cross-section 

Skill Sheet 3.3: Tanya Atwater 

1. Tanya Atwater came from a family of scientists—her father 

was an engineer and her mother a botanist. Atwater recalls 

many dinner discussions about science and she eventually 

shared in her parents’ passion. Atwater and her family went 

on many vacations. The family often found the most remote 

places to explore. This explains Atwater’s deep love for the 

outdoors. 

2. In 1967, Atwater began graduate school at the Scripps 

Oceanographic Institution in La Jolla, California. During this 

time, many exciting geological discoveries were being made. 

The concept of sea floor spreading was emerging, leading to 

the current theory of plate tectonics. 

3. While at Scripps, Atwater joined a research group that used 

sophisticated equipment to study the sea floor off of northern 

California. It was her first close look at sea floor spreading. 

Atwater also took twelve trips down to the ocean floor in the 

tiny submarine Alvin. She collected samples nearly 2 miles 

down on the ocean floor using mechanical arms. Atwater’s 

firsthand view through Alvin’s portholes gave her a better 

understanding of the pictures and sonar records she had 

previously studied. 

Skill Sheet 4.1: Solving Equations With One Variable 


1. w = 4.0 mm 

2. l = 0.8 m 

3. h = 8.00 cm 

4. d = 7.5 m 

5. s = 4.0 m/s 

6. t = 30 s 

7. t = 31.3 s 

8. D = 7.8 g/cm 3 

Skill Sheet 4.1: Problem Solving Boxes 

This skill sheet can be used throughout the school year to help 

students organize their work for questions or problems 

involving formulas and computation. 

Skill Sheet 4.1: Problem Solving with Rates 

1. 

2. 

3. 

4. 

365 days 

-------------------- 

1 year 

---------------------- 

1 foot 

12 inches 

$10.00 

--------------------------------- 

3 small pizzas 

3 boxes 

----------------------- 

36 pencils 

Page 11 of 57 

10. The Mid-Atlantic Ridge has a slow spreading rate, while the 

spreading rate of the East Pacific Rise is fast. Because the 

Mid-Atlantic Ridge is so slow, a valley has developed 

between the two separating plates. 

4. Propagating rifts are created when sea floor spreading centers 

realign themselves. This realignment is in response to 

changes in plate motion or uneven magma supplies. In the 

1980s, Atwater was part of a team that researched 

propagating rifts near the Galapagos Islands off the coast of 

Ecuador. She has also discovered many propagating rifts on 

the sea floor off the northeast Pacific Ocean and evidence of 

propagating rifts in ancient sea floor records worldwide. 

5. Atwater has been a geology professor at the University of 

California, Santa Barbara for over 25 years. Atwater also 

works with the media, museums, and teachers to educate 

them about the Earth. She has created presentations and an 

animated teaching film, “Continental Drift and Plate 

Tectonics,” that has been used by educators from the 

elementary school level through college. 

6. Answers may vary. Some of Alvin’s noteworthy trips include 

locating a hydrogen bomb accidentally dropped in the 

Mediterranean Sea (1966), several trips to the Mid-Atlantic 

Ridge and Galapagos Rift, surveying the sunken ocean liner 

Titanic (1986), and IMAX filming off of the San Diego coast 

for a deep sea feature production (2002). 

9. m = 1.1 g 

10. m = 4.5 g 

11. V = 113 cm 3 

12. V = 2.3 cm 3 


1. Force = 8 N 

2. p = 20 Pa 

3. p = 216 Pa 

4. p = 15,000 Pa 

5. 

---------------------------------------------------- 

360 miles 

18 gallons of gasoline 

6. 2,100 calories 

7. 1095 

-------------------------sodas 

year 

8. 725, 760 heatbeats 

-------------------------------------------week 

9. $27.48

10. 410 miles 

11. 6.6 miles 

--------------------hour 

12. 22.2 lbs 

13. 55 kg 

14. 5.4977 miles 

15. $280 

16. About 10 years 

17. 53 grams 

18. 0.11 miles 

-----------------------hour 

19. 270 pills 

20. 95 feet/sec 

Skill Sheet 4.1: Percent Error 

Table answers: 1. ≈ 0.43% 


(cm) 

Skill Sheet 4.1: Speed 

1. 17 km/hr 

2. 55 mph 

3. 4.5 seconds 

4. 5.9 hours; 490 mph 

5. 4.0 km 

6. 2.5 miles 

7. 4.5 meters 


a. 2.54 cm/inch 

b. 12 inches/min 

9. 6 km/hr 


a. 600 seconds 

b. 10 minutes 

11. 1,200 meters 


a. 42 km 

b. 9.3 km/hr 

Time from A to B 

(s) 

10 1.0050 

20 1.8877 

30 2.8000 

40 3.7850 

50 4.7707 

60 5.6101 

70 6.9078 

80 7.9648 

90 9.0140 

Page 12 of 57 

2. ≈ 3.30% 

3. ≈ 1.34% 

4. ≈ 0.16% 

5. ≈ 0.16% 


a. Avg. ≈ 17.18 s; percent error ≈ 5.06% 

b. Avg. = 38.39 s; percent error ≈ 9.61% 

c. Avg. = 67.91 s; percent error ≈ 0.68% 


a. 0.2 km/min 

b. 0.5 km/min 

c. 0.3 km/min faster by bicycle 

14. 12.5 km 

15. 40 minutes 

16. 90. km/hr 

17. 820 km/hr 

18. 32.5 km or 33 km 

19. 8 hours 

20. 633 km/hr 

21. 731 km/hr 

22. 1,680 km 

23. 3.84 × 10 5 km 

24. 2.03 × 10 4 seconds 

25. Answers for 25 (a)–(c) will vary. Having students write their 

own problems will further develop their understanding of 

how to solve speed problems.

Skill Sheet 4.1: Velocity 

1. 420. km/hr, north 


3. 224 minutes 


a. 1.62 m/s, west 

b. 1.62 m/s, east 

5. 16.0 hours 

6. 3.0 m/s, west 

Skill Sheet 4.2: Calculating Slope from a Graph 

Numbers correlate to graph numbers: 

1. 

2. 

3. m = -- Calculated using points (0,3) and (9,8) 

4. 

5. 

– 3 × 3 – 3 

m = -------------- = ----- 

6 × 2 4 

– 2 × 3 – 3 

m = -------------- = ----- 

4 × 2 4 

5 

9 

4 

m = -- = 2 

2 

3 

m = -- = 1 

3 

Page 13 of 57 


a. 4.5 m/s, south 

b. 4.5 m/s, north 

8. 22 seconds 

9. 0.36 miles/min, southwest or 22 mph, southwest 

10. 116 kilometers 

11. 3.9 km/hr, southeast 

12. 9.39 kilometers 

6. 

7. m =0 

8. 

9. m =2 

Skill Sheet 4.2: Analyzing Graphs of Motion with Numbers 


a. The bicycle trip through hilly country. 

b. A walk in the park. 

c. Up and down the supermarket aisles. 

10. 

– 2 

m = ----- = – 1 

2 

m 

3 

= -- 

4 

– 1 

m = 

----- 

2 


a. The honey bee among the flowers. 

b. Rover runs the street. 

c. The amoeba.

Skill Sheet 4.2: Analyzing Graphs of Motion without Numbers 

1. Little Red Riding Hood. Graph Little Red Riding Hood: 

2. The Tortoise and the Hare. Use two lines to graph both the 

tortoise and the hare: 

Skill Sheet 4.3: Acceleration 

1. –0.75 m/s 2 

2. –8.9 m/s 2 


Time (seconds) Speed (km/h) 

0 (start) 0 (start) 

2 3 

4 6 

6 9 

8 12 

10 15 

The acceleration of the ball is 1.5 km/hr/s. 

Skill Sheet 4.3: Acceleration and Speed-Time Graphs 

1. Acceleration = 5 miles/hour/hour or 5 miles/hour 2 

2. Acceleration = –2 meters/minute/minute or –2 

meters/minute 2 

3. Acceleration = 0 feet/minute/minute or 0 feet/minute 2 or no 

acceleration 


Skill Sheet 4.3: Acceleration due to Gravity 

1. velocity = –14.7 m/s 

2. velocity = 11.3 m/s 

3. velocity = –76.4 m/s 

4. velocity = –16 m/s; depth = 86 meters 

Page 14 of 57 

3. The Skyrocket. Graph the altitude of the rocket: 

4. Each student story will include elements that are controlled 

by the graphs and creative elements that facilitate the story. 

Only the graph-controlled elements are described here. 

a. The line begins and ends on the baseline, therefore Tim 

must start from and return to his house. 

b. The line rises toward the first peak as a downward curved 

line that becomes horizontal. This indicates that Tim’s 

pace toward Caroline’s house slowed to a stop. 

c. Then the line rises steeply to the first peak. This indicates 

that after his stop, Tim continues toward Caroline’s house 

faster than before. 

d. The first peak is sharp, indicating that Tim did not spend 

much time at Caroline’s house on first arrival. 

e. The line then falls briefly, turns to the horizontal, and then 

rises to a second peak. This indicates that Tim left, 

paused, and then returned quickly to Caroline’s house. 

f. The line then remains at the second peak for a long time, 

then drops steeply to the baseline. This indicates that after 

spending a long time at Caroline’s house, Tim probably 

ran home. 


5. 88 mph 

6. 22 m/s 

7. 7 m/s 2 

8. –1.9 mph/s 

9. 67 m/s 

10. 32 m/s 

11. 1.7 m/s 2 


13. –2.3 m/s 2 

a. Segment 1: Acceleration = 2 feet/second/second, 

or 2 feet/second 2 

b. Segment 2: Acceleration = 0.67 feet/second/second, 

or 0.67 feet/second 2 

5. Distance = 1,400 meters 

6. Distance = 700 feet 

7. Distance = 75 kilometers 

5. height = 11 meters; yes 

6. time = 5.6 seconds 

7. time = 7.0 seconds

Skill Sheet 5.1: Ratios and Proportions 

1. 6 tablespoons; 2 eggs 

2. 3 / 4 cup; 1 / 3 teaspoon 

3. 1 / 4 teaspoon; 3 / 4 cup 

Skill Sheet 5.1: Internet Research 


1. Example answer: “science museums” + “South Carolina” not 

“Columbia” 

2. “dog breeds” + “inexpensive” 

3. “producing electricity” not “coal” not “natural gas” 


1. Answers will vary. Sites that may be authoritative include 

non-profit sites (recognizable by having “org” as the 

extension in the web address) or government sites such as 

www.nasa.gov (recognizable by the “gov” extension address) 

or college/university websites (recognizable by the “edu” 

extension address). These sites often provide information to 

large, diverse groups and are not typically supported by 

advertising. Sites that are supported by advertising can be 

Skill Sheet 5.1: Bibliographies 


Skill Sheet 5.1: Mass vs. Weight 

1. 15 pounds 

2. 2.6 pounds 

3. 7.0 kilograms 

4. Yes, a balance would function correctly on the moon. The 

unknown mass would tip the balance one-sixth as far as it 

would on Earth, but the masses of known quantity would tip 

the balance one-sixth as far in the opposite direction as they 

did on Earth. The net result is that it would take the same 

amount of mass to equalize the balance on the moon as it did 

on Earth. (In the free fall environment of the space shuttle, 

however, the masses wouldn’t stay on the balance, so the 

balance would not work). 


a. As the elevator begins to accelerate upward, the scale 

reading is greater than the normal weight. As the elevator 

accelerates downward, the scale reads less than the 

normal weight. 

Page 15 of 57 

4. Table answers: 

Sugar 

3 /8 cup 

Butter 3 tablespoons 

Milk 1 tablespoon 

Chocolate chips 1 cup 

Eggs 

Vanilla extract 

1 egg 

Baking soda 

Salt 

1 /2 teaspoon 

1 /6 teaspoon 

1 /8 teaspoon 

Confectioner’s sugar 1 tablespoon 

5. To make 16 brownies, you need two eggs and 2 tablespoons 

of sugar. Therefore, to make 8 brownies, you only need 1 of 

each unit for each ingredient: 1 egg and 1 tablespoon of sugar. 

6. Since 8 brownies requires 1 cup of chocolate chips, 3 cups of 

chocolate chips will make 24 brownies. 

7. 1.5 teaspoons vanilla are needed to make 24 brownies. 

authoritative, but may be biased in the information presented. 

Another characteristic of authoritative sites are that they are 

actively updated on a regular basis. 

2. Answers will vary. Reasons for why a source may not seem to 

be authoritative include: the author of the site is not affiliated 

with an organization and does not have obvious credentials, 

and the information seems to be one-sided. Many science 

topic searches will lead to student papers published on the 

Internet. These may contain mistakes, or they may have been 

written by a younger student. 

3. Answers will vary. Intended audiences can be young children, 

pre-teens, teenagers, adults, or select groups of people 

(women, men, people who like dogs, etc.). 


b. When the elevator is at rest, the scale reads the normal 

weight. 

c. The weight appears to change because the spring is being 

squeezed between the top and the bottom of the scale. 

When the elevator accelerates upward, it is as if the 

bottom of the scale is being pushed up while the top is 

being pushed down. The upward force is what causes the 

spring to be compressed more than it is normally. When 

the elevator accelerates downward, the bottom of the scale 

provides less of a supporting force for the feet to push 

against. Therefore, the spring is not compressed as much 

and the scale reads less than the normal weight.

Skill Sheet 5.1: Mass, Weight, and Gravity 


a. 22 newtons 

b. 8.1 newtons 

c. 8.9 N/kg 


a. 65 kilograms 

b. 640 newtons 

c. 240 newtons 

Page 16 of 57 


a. 23.10 N/kg 

b. 0.6 N/kg 

c. 4.9 newtons 


a. 195,700 newtons 

b. 19,970 kilograms 

c. 146,800 newtons 

d. weight of toy-filled boxes = 48,900 newtons. 

mass of toy-filled boxes = 4,990. kg 

⎛ ⎞ i 

⎜ ⎟ 

⎝ ⎠ 

Skill Sheet 5.1: Gravity Problems 

Table 1 answers: 1. 9.5 pounds on Neptune 

Planet Force of gravity in Value compared to 2. 1,030 newtons on Saturn 

Newtons (N) Earth’s gravity 3. The baby weighs 45 newtons on Earth which is equal to 10.04 

Mercury 

Venus 

Earth 

Mars 

Jupiter 

3.7 

8.9 

9.8 

3.7 

23.1 

0.38 

0.91 

1 

0.38 

2.36 

pounds. 

4. Venus, Jupiter, Neptune, Pluto, then Saturn 

5. Answer: 

−11 

2 24 26 

6.67 × 10 Nm (6.4× 10 )(5.7 × 10 ) 

Gravity = 2 11 2 

kg 

(6.52× 10 ) 

Saturn 9.0 0.92 

17 

= 5.72× 10 N 

Uranus 8.7 0.89 

Neptune 11.0 1.12 

Pluto 0.6 0.06 

Skill Sheet 5.1: Universal Gravitation 

1. F =9.34× 10 –6 N. This is basically the force between you 

and your car when you are at the door. 

2. 5.27 × 10 –10 N 

3. 4.42 N 

4. 7.36 × 10 22 kilograms 


Skill Sheet 5.2: Friction 


a. rolling friction 

b. Sliding friction is generally greater than rolling friction, 

so it would probably take more force to transport the 

blocks in the sled. 

c. The friction force would increase, because more blocks 

would mean more weight force squeezing the two 

surfaces together. 

d. static friction 


a. viscous friction 

b. The friction force would increase because the boat would 

sit lower in the water. 


a. rolling friction and air friction 

Skill Sheet 5.3: Equilibrium 

1. 142 N 

2. A is 40 N; B is 8 N 

3. 340 N 

a. 9.8 N/kg = 9.8 kg-m/sec 2 -kg = 9.8 m/sec 2 

b. Acceleration due to the force of gravity of Earth. 

c. Earth’s mass and radius. 

6. 1.99 ×10 20 N 

7. 4,848 N 

8. 3.52 × 10 22 N 

b. rolling friction 


a. Student responses will vary. Encourage students to look 

for a sports car rather than a professional racing car. 

Racing car spoilers may serve a different purpose. 

b. Sports car spoilers are generally designed to increase 

down force on the rear of the car, causing greater friction 

between the rear tires and the road. 

c. Spoilers on hybrid cars and sport utility vehicles are 

usually designed to create a smoother, less turbulent 

airflow over the rear of the vehicle. This reduces drag (air 

friction). Sports car spoilers are most often designed to 

increase rolling friction, not to decrease air friction. 

Spoilers on different types of cars serve different 

purposes. 

4. From the outside of a balloon, two forces act inward. The 

elastic membrane of the balloon and the pressure of Earth’s 

atmosphere work together to balance the outward force of the 

helium compressed inside. Together with the elastic force,

atmospheric pressure near Earth’s surface applies enough 

force to maintain this equilibrium, but as the balloon rises, 

atmospheric pressure decreases. Although the inward force 

supplied by the elastic membrane remains unchanged, the 

decreasing atmospheric pressure force causes an imbalance 

with the outward force of the contained helium and the 

balloon expands. At some point, the membrane of the balloon 

reaches its elastic limit and bursts. 

Skill Sheet 6.1: Net Force and Newton’s First Law 

1. When at rest, the cart experiences a normal force of 105 N 

and its weight of –105 N. 

2. The net force on the cart is +20 N. While the cart is on the 

slippery margarine, it is not moving at constant velocity since 

it is experiencing a net force (acceleration). 

3. The normal force on the cart after it is loaded with groceries is 

+180 N. 

Skill Sheet 6.1: Isaac Newton 

1. The isolation due to the Plague allowed Newton to focus on 

his scientific work, free from the distractions of university 

life. However, most scientists learn a great deal from 

discussing their ideas with peers. Collaboration also enables 

experimental scientists to test a greater number of hypotheses. 

2. Newton was an active member of the scientific community at 

Cambridge for just under 30 years. In that time, he made great 

strides in understanding light and optics, planetary motion, 

universal gravitation, and calculus. He made extraordinary 

contributions to many scientific fields during those years. 

3. Example answer: Newton’s first law says that unless you 

apply an unbalanced force to an object, the object will keep 

on doing what is was doing in the first place. So a rolling ball 

will keep on rolling until an unbalanced force changes its 

motion, while a ball that is not moving will stay still unless 

acted on by an unbalanced force. 

Skill Sheet 6.2: Newton’s Second Law 

1. 2.100 m/s2 2. 83 m/s2 3. 82 N 

4. 6 kg 

5. 9800 N 

6. 900 kg 

7. 1.9 m/s2 Page 17 of 57 

4. Gravity accelerates the cart down the ramp. 

5. The friction force is greater on the rough blacktop than on the 

smooth tile. 

6. The line of twenty empty carts has twenty times as much 

inertia, so it takes a much greater force to get it moving. 

4. Example answer: The law of universal gravitation says that 

the force of attraction between two objects is directly related 

to the masses of the objects and inversely related to the 

distance between them. 

5. Newton’s law of universal gravitation. 

6. Newton claimed that 20 years earlier, he had invented the 

material that Leibnitz published. Newton accused Leibnitz of 

plagiarism. Most historians today agree that the two 

developed the material independently, and therefore they are 

known as co-discoverers. 

Extra information: The famous legend of Newton’s apple tells 

of Newton sitting in his garden in Linconshire in 1666, 

watching an apple fall from a tree. He later noted that “In the 

same year, I began to think of gravity extending to the orb of 

the moon.” However, he did not make public his musings 

about gravity until the 1680’s, when he formulated his law of 

universal gravitation.

Skill Sheet 6.3: Applying Newton’s Laws 

Table answers are: 

Newton’s laws 

of motion 

The 

first 

law 

The 

second 

law 

The 

third 

law 

Write the law here in your 

own words 

An object will continue 

moving in a straight 

line at constant speed 

unless acted upon by an 

outside force. 

The acceleration (a) of 

an object is directly 

proportional to the 

force (F) on an object 

and inversely 

proportional to its mass 

(m). The formula that 

represents this law is 

For every action force 

there is an equal and 

opposite reaction force. 

Skill Sheet 6.3: Momentum 

1. 

2. 

3. 

4. 

5. 

a 

= 

--- 

F 

m 

35 m 

momentum 4,000 kg × ----------- 140,000 kg 

s 

m 

= = 

⋅ --s 

35 m 

momentum 1,000 kg × ----------- 35,000 kg 

s 

m 

= = ⋅ --s 

8 kg × speed 16 kg m 

= ⋅ --s 

2 m 

speed = -------s 

0.5 m 

mass × ------------ 0.25 kg 

s 

m 

= ⋅ --s 

mass = 0.5 kg 

45,000 kg m 

⋅ --s 

Example of the law 

A seat belt in a car 

prevents you from 

continuing to move 

forward when your car 

suddenly stops. The seat 

belt provides the “outside 

force.” 

A bowling ball and a 

basketball, if dropped from 

the same height at the 

same time, will fall to 

Earth in the same amount 

of time. The resistance of 

the heavier ball to being 

moved due to its inertia is 

balanced by the greater 

gravitational force on this 

ball. 

When you push on a wall, 

it pushes back on you. 

Skill Sheet 6.3: Momentum Conservation 

1. m = p/v; m = (10.0 kg·m/s) / (1.5 m/s); m = 6.7 kg 

2. v = p/m; v = (1000 kg·m/s) / (2.5 kg); v = 400 m/s 

3. p = mv 

(mass is conventionally expressed in kilograms) 

p = (0.045 kg)(75.0 m/s) 

p = 3.38 kg·m/s 

4. p (before firing) = p (after firing) 

m 1 v 1 + m 2 v 2 = m 3 v 3 + m 4 v 4 

400 kg(0 m/s) + 10 kg(0 m/s) = 400 kg(v 2 ) + 10 kg(20 m/s) 

0 = 400 kg(v2) + 200 kg·m/s 

(v 2 ) = (–200 kg·m/s)/400 kg 

(v 2 ) = –0.5 m/s 

Page 18 of 57 

1. The purse continues to move forward and fall off of the seat 

whenever the car comes to a stop. This is due to Newton’s first law 

of motion which states that objects will continue their motion unless 

acted upon by an outside force. In this case, the floor of the car is 

the stopping force for the purse. 

2. Newton’s third law of motion states that forces come in action and 

reaction pairs. When a diver exerts a force down on the diving 

board, the board exerts an equal and opposite force upward on the 

diver. The diver can use this force to allow himself to be catapulted 

into the air for a really dramatic dive or cannonball. 

3. Newton’s second law 

4. The correct answer is b. One newton of force equals 1 kilogrammeter/second 

2 . These units are combined in Newton’s second law 

of motion: F = mass × acceleration. 

5. 

6. 

0.30 m 

s 2 

--------------- 

F 

= ------------ 

65 kg 

F 

0.30 m 

s 2 

--------------- × 65 kg 20. kg m 

s 2 

⎞ 

⎛ 

⎠ 

⎝ 

= 

= ⋅ ---- 

2 kg ⋅ m 

2 

2 N m 

a = = 

sec 

= 0.2 

10 kg 10 kg sec 

7. The hand pushing on the ball is an action force. The ball provides a 

push back as a reaction force. The ball then provides an action force 

on the floor and the floor pushes back in reaction. Another pair of 

forces occurs between your feet and the floor. 

8. A force 

6. 

----------- 

30.m 

s 

7. The 4.0-kilogram ball requires more 

force to stop. 

8. 980 kg 

9. 

4.2 kg 

10. 

11. 

m 

⋅ --s 

15 m 

--s 

0.01 kg m 

⋅ 

--s 

5. p (before throwing) = p (after throwing) 

m 1 v 1 + m 2 v 2 = m 3 v 3 + m 4 v 4 

0 = m 1 (0.05 m/s) + 0.5 kg(10.0 m/s) 

m 1 = (–0.5 kg)(10.0 m/s)/ (0.05 m/s) 

Eli’s mass + the skateboard (m 1 ) = 100 kg 


a. p = mv + Δp; p = mv + FΔt 

p = (80 kg)(3.0 m/s) + (800 N)(0.30 s) 

p = 480 kg·m/s 

b. v = p/m; v = (480 kg·m/s)/80 kg; v = 6.0 m/s 


a. p = mv; p = (2000 kg)(30 m/s); p = 60,000kg·m/s 

2

. FΔt = mΔv 

F = (mΔv)/(Δt); F = (60,000 kg·m/s)/(0.72 s) 

F = 83,000 N 


a. P = (# of people)(mv); p =(2.0 × 10 9 )(60 kg)(7.0 m/s); 

p =8.4× 10 11 kg·m/s 

b. p (before jumping) = p (after jumping) 

m 1 v 1 + m 2 v 2 = m 3 v 3 + m 4 v 4 

0 = 8.4 × 10 11 kg·m/s + 5.98 × 10 24 (v 4 ); 

(v 4 ) = (–8.4 × 10 11 kg·m/s)/ 5.98 × 10 24 

Earth moves beneath their feet at the speed 

v 4 = –1.4 × 10 –13 m/s 

Skill Sheet 6.3: Collisions and Momentum Conservation 

1. p = mv; p = (100.kg)(3.5m/s); p = 350kg·m/s 

2. p = mv; p = (75.0kg)(5.00m/s); p = 375kg·m/s 

3. Answer: 

p (before coupling) = p (after coupling) 

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )(v 3+4 ) 

(2000 kg)(5m/s) + (6000 kg)(–3m/s) = (8000 kg)(v 3+4 ) 

v 3+4 = –1m/s or 1m/s west 

4. Answer: 

p (before collision) = p (after collision) 

m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4 

(4 kg)(8m/s) + (1 kg)(0m/s) = (4 kg)(4.8m/s) + (1kg)v 4 

v 4 = (32kgm/s – 19.2kg-m/s)/(1kg); v 4 = 12.8m/s or 13m/s 

5. Answer: 

p (before shooting) = p (after shooting) 

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )(v 3+4 ) 

(0.0010 kg)(50.0 m/s) + (0.35 kg)(0 m/s) = (0.351kg)(v 3+4) 

(v 3+4 ) = (0.050kg-m/s)/ (0.351kg); (v 3+4 ) = 0.14 m/s 

6. Answer: 

p (before tackle) = p (after tackle) 

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )(v 3+4 ) 

(70 kg)(7.0 m/s) + (100 kg)(–6.0 m/s) = (170 kg)(v 3+4 ) 

(v 3+4) = (490kg·m/s – 600kg·m/s)/ (170kg) 

(v 3+4 ) = –0.65 m/s 

Terry is moved backwards at a speed of 0.65 m/s while Jared 

holds on. 

7. Answer: 

p (before hand) = p (after hand) 

m 1v 1 + m 2v 2 = (m 1+ m 2)(v 3+4) 

(50.0 kg)(7.00 m/s) + (100. kg)(16.0m/s) = (150 kg)(v 3+4 ) 

(v 3+4 ) = (350 kg·m/s + 1,600 kg·m/s)/150 kg 

(v 3+4) = 13 m/s 

Skill Sheet 6.3: Rate of Change of Momentum 

1. Force = 200,000 N. At this level of force, after a couple of 

hits with a wrecking ball, any impressive-looking wall 

crumbles to pieces. 

2. 3 seconds 

3. 250 N 

4. 750 N 

5. 75 million N 

6. The answers are: 

a. The force created on the egg is about: 

0.05 kg × 10 m/s 

---------------------------------------- = 500 N 

0.001 sec 

Page 19 of 57 


a. p = mv; p = (60 kg)(6.00 m/s); p = 360 kg·m/s 

b. v av = (v i + v f )/2; v av = (6.00 m/s + 0 m/s)/2 = 3.00 m/s 

Δt = d/ΔV; Δt = 0.10 m/3.00 m/s; Δt = 0.033 s 

FΔt = mΔV; F = (mΔV)/Δt; 

F = (60 kg)(6.00 m/s)/(0.033 s); F = 11,000 N 

10. Since the gun and bullet are stationary before being fired, the 

momentum of the system is zero. The “kick” of the gun is the 

momentum of the gun that is equal but opposite to that of the 

bullet maintaining the “zero” momentum of the system. 

11. It means that momentum is transferred without loss. 

8. Answer: 

p (before jump) = p (after jump) 

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )(v 3+4 ) 

(520 kg)(13.0 m/s) + (85.0 kg)(3.00 m/s) = (605 kg)(v 3+4); 

v 3+4 = (7,015 kg·m/s)/(605 kg) 

v 3+4 = 11.6 m/s 

9. Answer: 

p (before jumping) = p (after jumping) 

m 1 v 1 + m 2 v 2 + m 3 v 3 = m 1 v 4 + m 2 v 5 + m 3 v 6 

(45 kg)(1.00 m/s) + (45 kg)(1.00 m/s) + (70 kg)(1.00 m/s) = 

(45 kg)(3.00 m/s) – (45 kg)(4.00 m/s) + (70 kg)(v 6 ) 

160 kg·m/s = (–45 kg·m/s) + (70 kg)(v 6 ) 

(v 6) = (205 kg·m/s)(70 kg) 

(v 6 ) = 2.9 m/s 


a. Answer: 

p (before toss) = p (after toss) 

m 1 v 1 + m 2 v 2 = (m 3 + m 4 )(v 3+4 ) 

(0.10 kg)(v 1) + (0.10 kg)(0 m/s) = (0.20 kg)(15 m/s); 

(v 1 ) = (0.30 kg·m/s)(0.10 kg) 

(v 1 ) = 30. m/s 

b. Answer: 

p (before collision) = p (after collision) 

m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4 

(0.10 kg)(30 m/s) + (0.10 kg)(0 m/s) = (0.10 kg)(v 3) + 

(0.10 kg)(–30 m/s) 

(v 3 ) = (3.0 kg·m/s + 3.0 kg·m/s)/(0.10 kg) 

(v 3) = 60 m/s 

The block slides away at a much higher speed of v 3 = 60 

m/s. The “bouncy ball, by rebounding, has experienced a 

greater change in momentum. The block will experience 

this change in momentum as well. 

b. The force created on the egg by the person is: 

50 kg 9.8 m/s 

c. The force created by the person is close to the amount of 

force that broke the egg. Therefore, if the person fell on 

the egg, it would probably break. 

d. As a result the force will be 500 times smaller: 

e. The egg would probably not break if it fell on the pillow 

because the force is 500 times smaller than if it fell on the 

hard floor. 

2 

× = 490 N 

0.05 kg × 10 m/s 

---------------------------------------- = 

1 N 

0.5 s

Skill Sheet 7.1: Mechanical Advantage 

1. 4 

2. 0.4 

3. 100 newtons 

4. 25 newtons 


6. 26 newtons 

Skill Sheet 7.1: Mechanical Advantage of Simple Machines 

1. 5 

2. 1.5 

3. 0.5 meters 

4. 4.8 meters 

5. 0.4 

6. 0.8 meters 

7. 0.25 meters 

Skill Sheet 7.1: Work 

1. Work is force acting upon an object to move it a certain 

distance. In scientific terms, work occurs ONLY when the 

force is applied in the same direction as the movement. 

2. Work is equal to force multiplied by distance. 

3. Work can be represented in joules or newton·meters. 


a. No work done 

b. Work done 

c. No work done 

d. Work done 

e. Work done 

5. 100 N·m or 100 joules 


7. 100,000 N·m or 100,000 joules 

8. 50 N·m to lift the sled; no work is done to carry the sled 

9. No work was done by the mouse. The force on the ant was 

upward, but the distance was horizontal. 

Skill Sheet 7.1: Types of Levers 

Part 1 and 2 answers: 

1. 2nd class lever 

Page 20 of 57 

7. 3 


9. 1.5 


a. 1,500 newtons 

b. 2 meters 

8. 6.7 

9. 2 meters 

10. 12 meters 

11. 2.4 

12. 6 newtons 


14. 4 meters 

10. 10,000 joules 


a. 1.25 meters 

b. 27 pounds 

12. 2,500 N or 562 pounds 

13. 1,500 N 


15. 225 N·m or 225 joules 

16. 0.50 meters 


a. No work was done. 

b. 100 N·m or 100 joules 


a. No work is done 

b. 11 N·m or 11 joules 

c. 400 N·m or 400 joules (Henry did the most work.) 

2. 1st class lever 

3. 3rd class lever 

Answers for (4) include answers for (1)–(4) in Part 2:

4. Two examples: 

Skill Sheet 7.1: Gear Ratios 

1. 9 turns 

7. Answers for the table are: 

2. 1 turn 

Table 2: Setup for three gears 

3. 4 turns 

Set Gears Number Ratio 1 Ratio 2 

4. 10 turns 

5. 6 turns 

6. Answers for the table are: 

Table 1: Using the gear ratio to calculate number of turns 

up 

1 Top gear 

of 

teeth 

12 

(top gear: 

middle 

gear) 

(middle 

gear: bottom 

gear) 

Input 

Gear 

(# of teeth) 

Output 

Gear 

(# of teeth) 

Gear 

ratio 

(Input Gear: 

Output Gear) 

How many 

turns does 

the output 

gear make if 

the input 

gear turns 3 

times? 

How many 

turns does the 

input gear 

make if the 

output gear 

turns 2 times? 

2 

Middle 

gear 

Bottom 

gear 

Top gear 

24 

36 

24 

1 

-- 

2 

2 

-- 

3 

24 

36 

24 

12 

1 

3 

3 

9 

2 

0.67, or 2/3 

of a turn 

Middle 

gear 

Bottom 

36 

12 

2 

-- 

3 

3 

-- 

1 

24 36 0.67, or 2/3 2 3 

gear 

48 36 1.33, or 4/3 4 1.5 

3 Top gear 12 

24 48 0.5, or 1/2 1.5 4 

Middle 

gear 

Bottom 

gear 

48 

24 

1 

-- 

4 

4 

-- 

2 

4 Top gear 24 

Middle 

gear 

Bottom 

gear 

48 

36 

1 

-- 

2 

4 

-- 

3 

Page 21 of 57 

Total gear ratio 

(Ratio 1 × Ratio 2) 

1 

-- 

3 

2 

-- 

1 

1 

-- 

2 

2 

-- 

3

8. The middle gear turns left. The bottom gear turns right. 

9. 3 times 

10. 4 times 

Skill Sheet 7.1: Levers in the Human Body 

Lever A: 

1. Type of lever: Third-class lever. 

2. This lever is used to lift objects. 

Lever B: 

Skill Sheet 7.1: Bicycle Gear Ratios Project 

Students evaluate the gear ratios of their own bicycles to 

complete this project. Answers will vary. 

Skill Sheet 7.2: Potential and Kinetic Energy 

1. First shelf: 5.0 newton-meters 

Second shelf: 7.5 newton-meters 

Third shelf: 10. newton-meters 


a. 588 newtons 

b. 1.7 meters 

c. 5.8 m/s 

Skill Sheet 7.2: Identifying Energy Transformations 

1. (1) Chemical energy from food to kinetic energy to elastic 

energy; (2) chemical energy from food to kinetic energy; (3) 

elastic energy to kinetic energy. 

2. Electrical energy to radiant (microwave) energy to kinetic 

energy (increased movement of molecules in the soup, which 

increases the soup’s temperature). 

3. Chemical energy from food to kinetic energy (as Dmitri 

operates the pump) to pressure energy. 

Page 22 of 57 

11. 1/2 time 

12. 6 times 

3. Type of lever: First-class lever. 

4. This lever is used to chew food. 

Lever C: 

5. Type of lever: Second-class lever. 

6. This lever is used to raise and lower the heel of the foot while 

standing. 


a. 450 joules 

b. 450 joules 

c. 46 meters 

4. 25,000 joules 

5. 4 m/s 

6. 75 kilograms 

4. Chemical energy from the battery in controller to radiant 

energy (radio waves). Radio waves to electrical signal in car; 

chemical energy from car battery to kinetic energy as car 

moves. 

5. Chemical energy from food is transformed to kinetic energy 

which is transformed to potential energy as Adeline moves 

toward the top of the hill. As she coasts down the other side, 

potential energy is transformed to kinetic energy.

Skill Sheet 7.2: Energy Transformations—Extra Practice 


1. The potential energy of the stretched bungee cord is changed 

into the kinetic energy of the person bouncing back up. 

2. The potential energy of the football from its high point is 

changed into kinetic energy as it spirals down. 

3. In this case, radiant energy is converted to chemical energy in 

the battery, which is then converted to the electrical energy 

needed to run the calculator. Mechanical energy (kinetic or 

potential, is not being used in this case. 


1. The chemical potential energy of the wood is changed to 

radiant energy in the form of heat. Radiant energy is changed 

Skill Sheet 7.2: Conservation of Energy 

1. 0.20 meters 

2. 3.5 m/s 

3. 39.6 m/s 

4. 196,000 joules 

Skill Sheet 7.2: James Joule 

1. Perhaps because he thought that the pursuit of science was 

worthwhile. 

2. His father hired one of the most famous scientists of his time 

to tutor his sons. 

3. His interest was based upon his desire to improve the 

brewery. He wanted to make a more efficient electric motor to 

replace the old steam engines that they had at the time. 

4. His goal had been to replace the old steam engines with more 

efficient electric motors. He was not able to do that, however, 

he learned a great deal about electromagnets, magnetism, 

heat, motion, electricity, and work. 

5. Electricity produces heat when it travels through a wire 

because of the resistance of the wire. Joule’s Law also 

provided a formula so that scientists could calculate the exact 

amount of heat produced. 

Skill Sheet 7.3: Efficiency 

1. 27.1 percent 

2. 92 joules 

3. 100,000 joules 

4. 94.2 kilojoules 

Skill Sheet 7.3: Power 

1. 250 watts 

2. 50 watts 

3. 1,200 watts 

4. 1,500 watts 

5. 741 watts 

6. 720 watts 

7. work = 500 joules; power = 33 watts 

8. 1,800 seconds or 30 minutes 

Page 23 of 57 

into mechanical energy as the water boils, changes to steam, 

and makes the whistle vibrate, which causes vibrations in air 

molecules that we experience as sound. 

2. Nuclear energy is changed into electrical energy, which is 

changed into radiant energy (light to make the television 

picture) and mechanical energy (vibration of speakers) that 

causes vibration of air molecules that we experience as sound. 

3. The chemical potential energy of food is changed into 

mechanical energy of the bicyclist, which is changed into 

electrical energy of the generator, which is changed into 

radiant energy from the light. 

5. 10. meters 

6. 30. meters 


6. Joule believed that heat was a state of vibration caused by the 

collision of molecules. This contradicted the beliefs of his 

peers who thought that heat was a fluid. 

7. Joule knew that the temperature of the water at the bottom of 

the waterfall was warmer than the water at the top of the 

waterfall. He thought that this was true because the energy 

produced by the falling water was converted into heat energy. 

He wanted to measure how far water had to fall in order to 

raise the temperature of the water by one degree. Joule used a 

large thermometer to measure the temperature at the top of 

the waterfall and the temperature at the bottom of the 

waterfall. The experiment failed because the water did not fall 

the right distance for his calculations and there was too much 

spray from the waterfall to read the instruments accurately. 

8. Refrigeration 

9. The joule is the international measurement for a unit of 

energy. 



a. 2,025 million watts 

b. b. 39.5 percent 

6. 59 percent 

9. 2,160,000 joules 

10. 2,500 watts 

11. 90,000 joules 

12. work = 1,500 joules; time = 60 seconds 

13. force =25 newtons; power = 250 watts 

14. distance = 100 meters; power = 1,000 watts 

15. force = 333 newtons, work = 5,000 joules

Skill Sheet 7.3: Power in Flowing Energy 

1. Answers are given in table below: 2. Answers are: 

a. 1,800 J 

Force (N) Distance 

(m) 

Time 

(sec) 

Skill Sheet 7.3: Efficiency and Energy 

1. 55% 

2. 12% 


a. 91% 

b. Energy is lost due to friction with the track (which creates 

heat), air resistance, and the sound made by the track and 

wheels. 

Skill Sheet 8.2: Measuring Temperature 


a. 15°C 

b. 21°C 

c. 23.0°C, 30.0°C, 30.0°C, 31.5°C, 31.5°C 

Work (J) Power 

(W) 

100 2 5 200 40 

100 2 10 200 20 

100 4 10 400 40 

100 5 25 500 20 

50 20 20 1000 50 

20 30 10 600 60 

9 20 3 180 60 

3 25 15 75 5 

Skill Sheet 8.2: Temperature Scales 


a. 100°C 

b. 37°C 

c. 4.4°C 

d. –12.2°C 

e. 32°F 

f. 77°F 

g. 167°F 

2. 7.2°C 

3. 177°C 

4. 107°C 

5. 374°F 

6. 450°F 

7. The table shows that the friend in Europe thinks that the 

temperature is on the Celsius scale because 15°C is equal to 

59°F, a relatively warm air temperature. However, 15°F is a 

relatively cold air temperature, equivalent to –9.4°C. 

°F °C 

15°F = –9.4°C 

59°F = 15°C 

Skill Sheet 8.2: Reading a Heating/Cooling Curve 

1. The iron changed from liquid to gas between points D and E. 

2. The heat added to the iron was used to break the 

intermolecular forces between the iron atoms. 

Page 24 of 57 

b. 450 watts 


a. 60,000 J 

b. 2,000 W; 2.68 hp 


a. 36,750 J (37,000 J with correct significant figures) 

b. 20.4 W (20 W with correct significant figures) 

5. 200 W 


a. 5,000 seconds or 1.4 hours 

b. 8,640,000 J 

c. 17.3 apples 


a. 98,000 J 

b. 98,000 W; 131 hp 

8. 3.3 W 

c. The first hill is the tallest because a roller coaster loses 

energy as it moves along the track. No roller coaster is 

100% efficient. Unless there is a motor to give it 

additional energy, it will never be able to make it back up 

to a height as high as the first hill. 

4. 80% 

5. 278 m 

d. At 0°C, water changes from liquid to solid. At 100°C, 

water changes from liquid to gas. 

e. The liquid will expand so the level in the tube will 

increase. 

Answers to the “Reading the temperature” sections will vary. 


a. –283°F 

b. The melting point for this liquid is 35°F which is equal to 

1.7°C. The melting point for mercury is –38.9°C 

(–38.0°F). The unknown substance is not mercury, since 

its boiling point is not the same as that of mercury. 

Extension Answers: 

1. 184K to 242K 

2. –108°C 

3. –139°C 

4. –223°C 

5. 5,273K to 8,273K 

6. 10,273K 

7. 1,000,273K 

8. 15,000,273K 

9. 622K 

10. 900°F 

3. The melting temperature of iron is about 1,500°C.

4. The freezing temperature of iron is about 1,500°C. The 

melting and freezing temperatures of a substance are the 

same. 

5. The boiling temperature of iron is about 2,800°C. 

6. The boiling temperature of iron is about 2,700°C higher than 

the boiling temperature of water. That means it takes a lot 

more heat energy to break the intermolecular forces between 

iron atoms than those between water molecules. Iron’s 

intermolecular forces are much stronger than water’s. 

7. Freezing occurred between points B and C. 

8. The freezing and melting temperatures are the same—69°C. 

9. The melting temperature of stearic acid is higher than water’s 

melting temperature. The intermolecular forces between 

Skill Sheet 9.1: Specific Heat 

1. Gold would heat up the quickest because it has the lowest 

specific heat. 

2. Pure water is the best insulator because it has the highest 

specific heat. 

3. Silver is a better conductor of heat than wood because its 

specific heat is lower than that of wood. 

Skill Sheet 9.1: Using the Heat Equation 

1. 323 J 

2. 588 J 

3. 2,243 J 

4. The gold would cool down fastest. It has to release only 323 J 

of energy to return to its original temperature. 

Skill Sheet 9.2: Heat Transfer 

Definitions: 

Heat conduction: The transfer of heat by the direct contact of 

particles of matter. 

Convection: The transfer of heat by the motion of matter, 

such as by moving air or water. 

Thermal radiation: Heat transfer by electromagnetic waves, 

including light. 

1. Conduction. The water molecules collide with the frozen 

shrimp, transferring thermal energy by direct contact. 

2. Radiation and heat conduction. Heat from the Sun is radiated 

to Earth. The black asphalt absorbs more of this radiation than 

the light-colored sidewalk. Heat is transferred from the 

sidewalk and the asphalt to Juan’s feet by the process of heat 

conduction. Since the sidewalk absorbed more heat, it can 

transfer more heat to Juan’s feet. 

3. Convection. A thermal is a convection current in the 

atmosphere. 

4. Radiation and convection. the hot space heater emits thermal 

radiation, and convection currents distribute the heat 

throughout the room. 

Page 25 of 57 

stearic acid molecules are stronger than those between water 

molecules. That’s why it would take more heat energy to melt 

stearic acid. 

10. Yes, a substance can definitely be cooled below its freezing 

temperature. The ice in the first graph started at –20°C. The 

iron started 1,500°C below its freezing temperature, and the 

stearic acid continued to cool well below its freezing 

temperature. The molecules in a solid have some kinetic 

energy at their freezing temperatures. Their kinetic energy 

slowly decreases as they cool down further. Absolute zero 

(–273°C) is the point at which molecules have the minimum 

possible kinetic energy. 

4. Aluminum, because it has the higher specific heat. 

5. 5°C × 4,184J/kg °C = 20,920 J 

6. At the same temperature, the larger mass of water contains 

more thermal energy. 

5. 711,280 J 

6. 440,000 J 

7. 5.6 °C 

8. 4,393,200 J 

Skill Sheet 10.1: Measuring Mass With a Triple-Beam Balance 

Answers will vary. 

Skill Sheet 10.1: Measuring Volume 


a. Sample student answer: The water level will rise so that it 

spills out of the spout. 

b. A fist-sized rock will displace more water because it is 

bigger and will sink (an acorn may float). 

collected. The volume of water that spills equals the volume of the object. 

5. Conduction. The mother duck is in direct contact with the 

eggs so the heat is transferred from her body directly to the 

eggs. 

6. Radiation. Thermal energy from the Sun is absorbed by the 

car. 

7. Conduction. The molecules of hot coffee collide with the 

molecules of cold milk. The average kinetic energy of the 

coffee molecules decreases, and the average kinetic energy of 

the milk molecules increases until thermal equilibrium is 

reached. The equilibrium temperature is lower than the initial 

temperature of the coffee. 

8. Convection. A sea breeze is a convection current in the 

atmosphere, created when air over the land is heated and 

rises. Then cool air from over the water rushes in to take its 

place, creating the sea breeze. 

9. Conduction. The heat from the water is transferred directly to 

the pipes, then to the marble floor, then to the feet. 

10. Conduction and convection. First the heat from the water is 

transferred to the pipes and then to the floor. Then convection 

currents circulate the heat from the floor to all parts of the 

room. 

c. The volume of spilled water equals the amount of water 

that is displaced by the object. 

d. Water is added to the displacement tank until it can hold 

no more without the water spilling out of the spout. Then 

an object is placed in the tank and the spilled water is

Skill Sheet 10.1: Calculating volume 


a. cm 3 or centimeters cubed 

b. 64 in 3 

c. Area is calculated using two dimensions (length and 

width). Volume is calculated using three dimensions 

(length, width, and height). 

d. 64 cubes each 1 cm 3 would fit 

Calculating volume of a rectangular prism: 

1. 24 cm 2 

2. 48 cm 3 

3. 90 cm 3 

Calculating volume of a triangular prism: 

1. 3 cm 2 

2. 18 cm 3 

3. 100 cm 3 

Calculating volume of a cylinder: 

1. 28.3 cm 2 

2. 170 cm 3 

3. 402 cm 3 

Calculating volume of a cone: 

Skill Sheet 10.1: Density 

1. 1.10 g/cm3 2. 0.870 g/cm3 3. 2.7 g/cm3 4. 920,000 grams or 920 kilograms 

5. 2,420 grams or 2.42 kilograms 

6. 1,025 grams or 1.025 kilograms 

7. 1,200 cm3 8. 29.8 cm3 9. 11.4 mL 

Skill Sheet 10.3: Pressure in Fluids 

1. 50,000 Pa 

2. 157,000 N 

3. 0.0015 m2 4. 5 m2 5. If the area of the input piston is doubled, the pressure 

transmitted by the system is cut in half. 

6. If the area of the input piston is doubled (and no other 

variables are changed), the output force is cut in half. 

Skill Sheet 10.3: Boyle’s Law 

1. 3.25 atm 

2. 36 m 3 

3. 563 kPa 

4. 570 liters 

5. 25 liters 

Skill Sheet 10.4: Buoyancy 

1. Sink 

2. Float 

3. 0.12 N 

4. 0.10 N 

5. The light corn syrup has greater buoyant force than the 

vegetable oil. 

6. 0.13 N 

Page 26 of 57 

1. 78.5 cm 2 

2. 628 cm 3 

3. 134 cm 3 ; this volume is one-third the value of the volume of 

the cylinder with similar dimensions. 

Calculating volume of a rectangular pyramid: 

1. 20 cm 2 

2. 40 cm 3 

3. 66.7 cm 3 

4. About 6.25 cm 

Calculating volume of a triangular pyramid: 

1. 6 cm 2 

2. 14 cm 3 

3. 50 cm 3 

4. 12.6 cm 

Calculating volume of a sphere: 

1. 268 cm 3 

2. 33.5 cm 3 

3. 523 cm 3 (assume 3.14 for pi) 


a. density = 960. kg/m 3 , HDPE 

b. 76,000 grams or 76 kilograms 

c. The volume needed is 0.11 m 3 ; 11 10-liter containers would 

be needed to hold the plastic 

d. HDPE, LDPE, PP (PS would probably be suspended in 

seawater) 

7. No, the output distance must be less than the input distance. 

Output work (output force × output distance) can never be 

greater than input work (input force × input distance). 

8. The woman’s force (540 N) remains constant whether she’s 

wearing high heels or snowshoes. But the area over which the 

force is applied is much greater with snowshoes than high 

heels. Since pressure = force ÷ area, the pressure applied to 

the floor by high heeled shoes is much greater than the 

pressure applied to the snow by the snowshoes. 

7. The buoyant force would be smaller if the gold cube were 

suspended in water. Student explanations may vary. A simple 

observation, such as “The water is thinner than the molasses” 

is acceptable, as well as the more sophisticated “The 

displaced water would weigh less than the displaced 

molasses” or “The water is less dense than the molasses.”

Skill Sheet 10.4: Charles’s Law 

1. 25.4 liters 

2. 22.8 liters 

Skill Sheet 13.2: Pressure-Temperature Relationship 

1. 0.27 atmospheres 

2. 1,000 K 

Skill Sheet 10.4: Archimedes 

1. Density: a property that describes the relationship between a 

material’s mass and volume. Buoyancy: A measure of the 

upward force a fluid exerts on an object. 

2. Sample answer: I, Archimedes, have a wide variety of skills 

to offer. First, I am an inventor of problem-solving devices, 

including a device for transporting water upward. I have also 

worked as a crime scene investigator for the king, uncovering 

fraud through scientific testing of materials. Furthermore, I 

am a writer with several treatises already published. I also 

have advanced skills in mathematics and can even estimate 

for you the number of grains of sand needed to fill the entire 

universe. 

3. In the treatise entitled “The Sand Reckoner,” Archimedes 

devised a system of exponents that allowed him to represent 

large numbers on paper—up to 8 × 10 63 in modern scientific 

notation. This was large enough, he said, to count the grains 

Skill Sheet 10.4: Narcís Monturiol 

1. Monturiol was motivated by the suffering of the coral divers 

he saw along the coast of Spain. The divers performed 

dangerous work to retrieve pieces of coral. They could drown, 

hurt themselves on rocks and coral, or be attacked by sharks. 

A submarine would provide a safer means of gathering coral. 

2. Ictineo I relied on human power to turn the propellers. It had a 

spherical inner chamber to withstand water pressure and an 

egg-shaped outer chamber for ease of movement. It also had a 

ventilator, two sets of propellers, and several portholes. 

Monturiol even created a backup system to ensure that the 

submarine could be raised to the surface in case of 

emergency. Ictineo I could dive to 20 meters and stayed 

underwater for nearly two hours. 

Ictineo II used steam power instead of human power to turn 

the propellers. Monturiol developed a chemical reaction to 

power the engine. This reaction also added oxygen to the 

Skill Sheet 10.4: Archimedes’ Principle 

1. If they are both submerged, then they both displace the same 

amount of water and have the same buoyant force acting on 

them. 

Page 27 of 57 


V1 T1 V2 T2 a. 6,114 mL 838 K 1,070 mL 147 K 

b. 3,250 mL 475°C 1,403 mL 50°C 

(748 K) 

(323 K) 

c. 10 L – 58°C 15 L 50°C 

(215 K) 

(323 K) 


P1 T1 P2 T2 a. 30.0 atm –100 °C 134 atm 500 °C 

(173 K) 

(773 K) 

b. 15.0 atm 25.0 °C 18.0 atm 85 °C 

(298 K) 

(360 K) 

c. 5.00 atm 488 K 3.00 atm 293 K 

of sand that would be needed to fill the universe. His 

assessment of the universe’s size was an underestimate, but 

he was the first to think of the universe being so large. 

4. A helium balloon floats in air because the air it displaces 

weighs more than the filled balloon. A balloon filled with air 

from someone’s lungs sinks because the combined weight of 

the latex balloon and the air inside is greater than the weight 

of the air it displaces. 

5. Inventions attributed to Archimedes include war machines 

(such as a lever used to turn enemy boats upside down), the 

Archimedes screw, compound pulley systems, and a 

planetarium. There is some debate about whether he invented 

a water organ and a system of mirrors and/or lenses to focus 

intense, burning light on enemy ships. Students can use the 

Internet or library to find more information and diagrams of 

the inventions. 

submarine. Ictineo II was longer than Ictineo I, had two 

engines, dove to 30 meters, and remained underwater for 

nearly seven hours. 

3. A replica of Ictineo I is located at the Marine Museum in 

Barcelona. A replica of Ictineo II can be found at Barcelona 

harbor. 

4. In 1862, Ictineo I was destroyed by a freight ship while 

anchored in Barcelona Harbor. 

5. Monturiol developed the following: A process to speed up the 

manufacturing of adhesive paper, a machine to copy letters, a 

stone cutter, and a meat preservative. 

6. Spain created a postage stamp in Monturiol’s honor. 

7. The Narcís Monturiol medal is an award given for 

“distinction in science and technology and for contributions 

to the scientific development of Catalonia.” 


a. 100 cm 3 

b. 0.98 N 

c. 0.98 N 

d. sink


a. 100 cm 3 

b. 13 N 

c. 13 N 

d. float 

4. In both cases, a material sinks in a fluid if it is more dense 

than the fluid. A material floats in a fluid if it is less dense 

than the fluid. 

Skill Sheet 11.1: Layers of the Atmosphere 

Skill Sheet 11.2: Gustave-Gaspard Coriolis 

1. Coriolis attended one of the best-known engineering schools 

in France. His exceptional ability coupled with great 

schooling provided him with a solid foundation for his 

thoughts, research, and studies. 

2. His first book presented mechanics in a way that could easily 

be applied. It was the foundation and establishment of 

applying the concept of work to the field of mechanics. 

Coriolis was intent on using and applying proper terms. He 

was the first to derive formulas expressing kinetic energy and 

mechanical work. 

3. As you are flying overhead, Earth is rotating from west to east 

beneath you. By the time you are ready to land, Earth has 

rotated far enough that Little Rock is east of your current 

position. 

4. In the northern hemisphere, the Coriolis effect bends winds to 

the right. In the southern hemisphere it bends winds to the 

left. 

5. Answers will vary, but should include the following: 

Trade winds are surface wind currents that move between 30 

degrees North latitude and the equator. The Coriolis effect 

bends the trade winds moving across the surface so they flow 

from northeast to southwest in the northern hemisphere and 

from southwest to northeast in the southern hemisphere. 

Skill Sheet 11.2: Degree Days 


1. Cooling degree day value = 88 – 65 = 23. 

2. Heating degree day value = 65 – 14 = 51. 

Page 28 of 57 


a. Floats 

b. Sinks 

c. Sinks 

d. Sinks 

Layer Distance from Earth’s surface Thickness Facts 

Troposphere 0–11 km 11 km Most of Earth’s water vapor, carbon dioxide, dust, 

airborne pollutants, and terrestrial life forms are 

found in this layer. 

The temperature drops as you go higher into the 

troposphere. 

Stratosphere 11–50 km 39 km The ozone layer is located here. 

The temperature increases as you go higher into 

the stratosphere. 

Mesosphere 50–80 km 30 km “Shooting stars” occur when meteors burn up in 

this layer. 

The mesosphere is the coldest layer of the 

atmosphere. 

Thermosphere 80—approx. 500 km 420 km Very low density of air molecules in this layer. 

Very high temperatures because sun’s rays hit here 

first. 

Exosphere 500 km—no specific 

outer limit 

undefined Lightweight atoms and molecules escape into 

space. 

Many man-made satellites orbit in this region, 

about 36,000 km above the equator. 

Polar easterlies form when the air over the poles cools and 

sinks, and spreads along the surface to about the 60 degree 

latitude. The polar wind is bent by the Coriolis effect and the 

air flows from northeast to southwest in the northern 

hemisphere, and from southeast to northwest in the southern 

hemisphere. Bands of cold air move away from the poles. 

Prevailing westerlies are created when air bends to the right 

due to the Coriolis effect. These winds blow towards the poles 

from the west and are bent to the right in the northern 

hemisphere and to the left in the southern hemisphere. 

6. His work was not accepted outside the field of mechanics 

until 1859 when the French Academy of Science arranged for 

a discussion on Earth’s rotation and its effects on water 

currents. His work on Earth’s rotation was discussed and 

linked to the field of meteorology in the late 1800’s early 

1900’s. 

7. Coriolis was able to connect theory with application in each 

of these books. The billiard book was published in 1835 and 

provided the mathematical theory of spin, friction, and 

collision in the game of billiards. Coriolis discussed how 

physics determines and explains the game of billiards. The 

Treatise book was published after his death in 1944. 

3. On July 22, 2002 the heating degree day value was zero. On 

January 22, 2003 the cooling degree day value was zero.


1. Answers: 

Day High Low Average Heating Cooling 

temp temp temp 2 degree day degree day 

1 73 61 67 0 2 

2 63 52 58 7 0 

3 70 44 57 8 0 

4 65 52 59 6 0 

5 83 58 71 0 6 

6 79 59 69 0 4 

7 74 60 67 0 2 

8 71 53 62 3 0 

9 90 70 80 0 15 

10 82 62 72 0 7 

11 65 52 59 6 0 

12 71 52 62 3 0 

13 74 56 65 0 0 

14 75 60 68 0 3 

Two week totals: 33 39 

2. St. Louis residents were more likely to use heating systems on 

six days and more likely to cool their homes on seven days. 

However, many of these days had such small degree day 

values that residents may have used either system only rarely. 

The most likely day to use energy for heating or cooling was 

May 9, with a cooling degree day value of 15. 


1. Total heating degree day value: 33 

2. Total cooling degree day value: 39 

3. The monthly total heating degree day value for May 2003 was 

33+31, or 64. The monthly total cooling degree day value was 

39+32, or 71. 

4. May 2003’s total heating degree day value was 15 less than 

normal, and its total cooling degree day value was 43 less 

than normal. With average temperatures closer to 65°F, St. 

Louis residents probably used less energy for heating and 

cooling in May than is usually needed. 

Skill Sheet 11.3: Joanne Simpson 

1. Simpson is the first woman to earn a Ph.D. in meteorology, 

the first person to create a computerized cloud model, and the 

first woman to have served as president of the American 

Meteorological Society. 

2. Simpson faced discrimination based on the fact that she was a 

woman. At the end of the war, most women returned home after 

temporarily filling the roles of men away during the war. 

Simpson was not one of those women. She continued on with 

her studies after teaching meteorology to aviation cadets. She 

earned a master’s degree and was so interested in meteorology 

that she wanted to go on for a Ph.D. Her advisor and the all-male 

faculty at her university did not support a woman going on for 

an advanced degree. They felt that women were unable to do the 

work which included shifts and flying planes. Simpson did 

finally find an advisor to support her Ph.D., but even he had 

negative comments about her topic. Simpson did have difficulty 

finding a job, but eventually landed a position as an assistant 

professor of physics. She continued to move into numerous 

positions and did not let others’ opinions and comments stop her 

career pursuits. 

3. Students should comment on Simpson’s determination 

despite the obstacles she faced along her journey to complete 

her degree and to work in the field of meteorology. Students 

will understand that if you really want to achieve a goal, you 

need to stay focused, work hard, and not be discouraged by 

negative opinions along the way. 

Page 29 of 57 


1. Graph: 

2. January 

3. July 


a. I chose May because the total heating and cooling degree 

day values are significantly less than any other month, and 

because many days with low degree day values probably 

won’t require any actual heating or cooling. 

b. You would need to know how much energy it takes to run 

each system per hour, the type of fuel used to run it, and 

the cost of the fuel. Natural gas and heating oil are 

commonly used for home heating systems, while 

electricity (most commonly generated by coal or natural 

gas) is commonly used for air conditioning systems. 

Electricity is often more expensive than natural gas or 

heating oil. As a result, cooling a home is often more 

expensive than heating it. 

4. A slide rule is a mechanical tool used to calculate complicated 

mathematical problems involving multiplication, divisions, 

square roots, cube roots, and trigonometry. The invention of 

the slide rule dates back to the 16th century. The slide rule, a 

handheld tool, was used commonly in science and 

engineering. The scientific calculator and computers made 

the slide rule obsolete. 

5. This is the highest award given by the American 

Meteorological Society for atmospheric science including 

meteorology, climatology, atmospheric physics, and 

atmospheric chemistry. It is named after Carl-Gustaf Rossby, 

a leader in the fields of oceanography and meteorology. He 

was also the 2nd recipient of this award. 

6. Woods Hole Oceanographic Institute (WHOI) is located in 

Woods Hole, Massachusetts on Cape Cod. Scientists at 

WHOI study oceans, their function, and their interaction with 

the Earth. WHOI provides opportunities for research and 

higher education. Students can visit the WHOI website on the 

Internet for more information. 

7. Students can locate hot tower clouds in scientific articles or 

websites. Hot towers are commonly associated with 

hurricanes. The NASA website provides some specific 

information about hot towers.

Skill Sheet 11.3: Weather Maps 

Sample table with answers: 

City High Low Temp difference Sky cover Pressure 

Seattle 72 54 18 Partly 

cloudy 

High 

Los Angeles 85 68 17 Sunny High 

Las Vegas 108 81 27 Pcldy High 

Phoenix 108 86 22 Pcldy High 

Atlanta 89 66 23 Pcldy Low 

Tampa 88 74 14 T-storms Low 

San Francisco 76 56 20 Sunny Low 

Oklahoma City 101 74 27 Pcldy High 

New Orleans 94 76 18 T-storms Low 

Kansas City 91 70 21 Pcldy Low 

Tucson 103 76 27 Pcldy High 

Denver 94 62 32 Pcldy Low 

Dallas 105 78 27 Sunny High 

Houston 98 76 22 Pcldy High 

Minneapolis 86 64 22 Sunny High 

Memphis 94 73 21 Sunny High 

Chicago 85 66 19 T-storms Low 

Miami 93 75 18 T-storms Low 

New York 73 63 20 T-storms Low 

Baltimore 78 70 8 T-storms Low 

1. The highest temperatures (daily high over 95°F) are in the 

lower latitudes such as Las Vegas, Phoenix, Tucson, Dallas, 

and Houston. The coolest temperatures (daily high under 

82°F) are found in Seattle, Chicago, and New York. These 

cities are at higher latitudes. The Sun is more directly 

overhead in lower latitude regions, and it is lower on the 

horizon and therefore less intense at midday in the higher 

latitude regions. 

Skill Sheet 11.3: Tracking a Hurricane 

Map answers: 


2. Students may mention Florida or Cuba as likely hurricane 

watch areas. The Bahamas should be mentioned as a hurricane 

Page 30 of 57 

2. Even though Los Angeles is the southern part of the 

continent, its high temperature was only 85°F. This is due to 

the cooling effect of the Pacific Ocean. Chicago is farther 

south than Minneapolis, but it is cooler because it sits on the 

shore of Lake Michigan. Denver, with its Rocky Mountain 

location, cools down to a nighttime low of 62°F in the 

summer. 

3. On the map, the thickest cloud cover is in the Northeast, 

where it cools Baltimore and New York. Baltimore and 

Kansas City are near the same latitude, but Kansas City (with 

less cloud cover) was 13°F warmer. During the day, the 

clouds reflect some of the sun’s heat away. 

4. Sample answers: The high-pressure regions center on 

Oregon, New Mexico, and Quebec. The low-pressure regions 

center on Wyoming, North Dakota, and North Carolina. 

5. See the table for answers. 

6. High pressure regions tend to have sunny weather, since less 

air is rising, cooling, and condensing. Humidity is much 

lower in these regions. 

7. Low-pressure regions tend to be overcast and/or stormy. The 

humidity is higher. 

8. Fronts are associated with low pressure regions. Fronts tend 

to bring precipitation. 

9. Cold fronts are associated with stormy areas. Warm fronts 

tend to be accompanied by bands of light precipitation. 

10. The air in a low-pressure region rises. The air in a high 

pressure region sinks. 

11. In a low pressure region, warm, moist air can be carried 

upward by convection. As the air cools, water condenses into 

clouds and precipitation. 

12. A low-pressure region is a good place for a volume of air to 

reach the dew point temperature because the warm, moist air 

in this region rises. As this air rises, it cools to the dew point 

temperature. The result is that the water in the air mass 

condenses, clouds form, and eventually precipitation occurs. 

warning area. Here are the actual watches and warnings issued 

by the Tropical Prediction Center for this time period: 

Date Time (GMT) Action Region 

8/22/1992 1500 Hurricane watch Northwest Bahamas 

8/22/1992 2100 Hurricane warning Northwest Bahamas 

8/22/1992 2100 Hurricane watch Florida east coast from 

Titusville through the 

Florida keys 

8/23/1992 0600 Hurricane warning Central Bahamas 

8/23/1992 1200 Hurricane warning Florida east coast from 

Vero Beach southward 

through the Florida keys 

8/23/1992 1200 Hurricane watch Florida west coast south 

of Bayport including 

greater Tampa area to 

north of Flamingo 

Parts 3, 4, and 5 answers: 

3.2 The Bahama islands. Note: The National Hurricane Center 

reported that landfall occurred at the northern Eleuthera 

Island, Bahamas. 

4.2 Southern Florida. Note: The National Hurricane Center 

reported that landfall occurred at Homestead Air Force Base, 

Florida. 

5.2 Louisiana. Note: The National Hurricane Center reported that 

landfall occurred at Point Chevreuil, Louisiana.

Skill Sheet 12.1: Structure of the Atom 

1. Answers are: 2. Answers are: 

a. hydrogen-2: 1 proton, 1 neutron 

What is this element? How many electrons does 

the neutral atom have? 

Skill Sheet 12.1: Atoms and Isotopes 


1. protium has 0 neutrons; deuterium has 1 neutron; tritium has 

2 neutrons 


a. 3 

b. Lithium 

c. 7 

d. 

What is the mass 

number? 

lithium 3 7 

carbon 6 12 

hydrogen 1 1 

hydrogen 

(a radioactive isotope, 

3H, called tritium) 

1 3 

beryllium 4 9 

Li 

7 

3 

Skill Sheet 12.1: Ernest Rutherford 

1. Alpha particle: a particle that has two protons and two 

neutrons (also known as a helium nucleus). Beta particle: An 

electron emitted by an atom when a neutron splits into a 

proton and an electron. 

2. For one atom to turn into another kind of atom, the number of 

protons in the nucleus must change. This can happen when an 

alpha particle is ejected (two protons are lost then) or when a 

neutron splits into a proton and an electron (in that case the 

number of protons increases by one). 

3. Diagram: 

Skill Sheet 12.2: Electrons and Energy Levels 

1. Danish physicist Neils Bohr 

2. Energy levels can be thought of as similar to steps on a 

staircase. Electrons can exist only in one energy level or 

another and cannot remain between energy levels, just as a 

Page 31 of 57 

b. scandium-45: 21 protons, 24 neutrons 

c. aluminum-27: 13 protons, 14 neutrons 

d. uranium-235: 92 protons, 143 neutrons 

e. carbon-12: 6 protons, 6 neutrons 

3. Most of an atom’s mass is concentrated in the nucleus. The 

number of electrons and protons is the same but electrons are 

so light they contribute very little mass. The mass of the 

proton is 1,835 times the mass of the electron. Neutrons have 

a bit more mass than protons, but the two are so close in size 

that we usually assume their masses are the same. 

4. Yes, it has a proton (+1) and no electrons to balance charge. 

Therefore, the overall charge of this atom (now called an ion) 

is +1. 

5. This sodium atom has 10 electrons, 11 protons, and 

12 neutrons. 


1. Bromine-80 

2. Potassium-39 has 20 neutrons. 

3. Lithium-7 

4. Neon-20 has 10 neutrons. 

4. Rutherford’s planetary model suggested that an atom consists 

of a tiny nucleus surrounded by a lot of empty space in which 

electrons orbit in fixed paths. Subsequent research has shown 

that electrons don’t exist in fixed orbitals. The Heisenberg 

uncertainty principle tells us that it is impossible to know both 

an electron’s position and its momentum at the same time. 

Scientists now discuss the probability that an electron will 

exist in a certain position. Computer models predict where an 

electron is most likely to exist, and three-dimensional shapes 

can be drawn to show the most likely positions. The sum of 

these shapes produces the charge-cloud model of the electron. 

5. In the game of marbles, players “shoot” one marble at a group 

of marbles and then watch the deflection as collisions occur. 

This is a lot like what Rutherford was doing on a much, much 

smaller scale. Rutherford’s comment is reflective of his 

typical self-deprecating humor. While “playing with 

marbles,” he discovered the proton. 

6. Answers will vary. Students may wish to write about one of 

the following discoveries: Rutherford first described two 

different kinds of particles emitted from radioactive atoms, 

calling them alpha and beta particles. He also proved that 

radioactive decay is possible. He developed the planetary 

model of the atom, and was the first to split an atom. 

person can be on one step or another but not between steps 

except in passing. 

3. Energy levels are filled from the lowest (innermost) energy 

level outward. 

4. answers are:

a. b. c. 

d. e f. 

Skill Sheet 12.2: Neils Bohr 

1. Both Rutherford and Bohr described atoms as having a tiny 

dense core (the nucleus) surrounded by electrons in orbit. 

Bohr described the nature of the electrons’ orbits in much 

greater detail. 

2. Niels Bohr described 

electrons as existing in 

specific orbital pathways, 

and explained how atoms 

emit light. 

3. In Bohr’s model of the 

atom, the electrons are in 

different energy levels. 

Bohr’s model of the atom 

at right: 

4. An electron absorbs 

energy as it jumps from an 

inner orbit to an outer one. 

When the electron falls 

Skill Sheet 12.3: The Periodic Table 

1. Fluorine 

2. Argon 

3. Manganese 

4. Phosphorous 

5. Technetium 

6. The atomic number tells the number of protons in an atom of 

the element. 

7. Iron, 55.8 amu 

8. Cesium, 132.9 amu 

9. Silicon, 28.1 amu 

10. Sodium, 23.0 amu 

11. Bismuth, 209.0 amu 

12. The atomic mass tells the average mass of all known isotopes 

of an element, expressed in amu. 

13. The atomic mass isn’t always a whole number because it is an 

average mass of all known isotopes. 

14. The mass of an electron is too small to be significant. 

15. Alkali metals 

Page 32 of 57 

back to the inner orbit, it releases the absorbed energy in the 

form of visible light. 

5. Answers will vary. You may wish to ask students to research 

world events from the end of World War II to Bohr’s death in 

1962. Students should look for events that may have raised 

concerns in Bohr’s mind about the potential use/misuse of 

nuclear weapons. They might also choose to research Bohr’s 

own comments on the subject. 

16. Any two of the following: 

soft, silvery, highly reactive, combines in 2:1 ratio with 

oxygen 

17. Any three of the following: 

F, Cl, Br, I, At 

18. They are toxic gases or liquids in pure form, highly reactive, 

and form salts with alkali metals. 

19. In the far right column 

20. They rarely form chemical bonds with other atoms. 

21. See figure 12.20, student text. 

22. as above 

23. as above 

24. as above 

25. as above 

26. Hydrogen 

27. Fluorine 

28. Carbon 

29. Sodium 

30. Chlorine

Skill Sheet 13.1: Dot Diagrams 

Part 1 answers: Part 2 answers: 

Element Chemical Total No. of Valence Dot Diagram Elements Dot Diagram for Each Dot Diagram for 

Symbol Electrons Electrons 

Element Compound Formed 

Potassium K 19 1 

Chemical 

Formula 

Na and F NaF 

Nitrogen N 7 5 

Carbon C 6 4 

Beryllium Be 4 2 

Skill Sheet 13.2: Finding the Least Common Multiple 

1. 21 

2. 24 

3. 45 

4. 50 

5. 80 

Neon Ne 10 8 

Sulfur S 16 6 

6. 147 

7. 108 

8. 315 

9. 880 

10. 192 

Skill Sheet 13.2: Chemical Formulas 

Answers: 

Element Oxidation No. Element Oxidation No. Chemical Formula for Compound 

Potassium (K) 1+ Chlorine (Cl) 1– KCl 

Skill Sheet 13.2: Naming Compounds 

Page 33 of 57 

Br and Br Br 2 

Mg and O MgO 

Calcium (Ca) 2+ Chlorine (Cl) 1– CaCl2 Sodium (Na) 1+ Oxygen (O) 2– Na2O Boron (B) 3+ Phosphorus (P) 3– BP 

Lithium (Li) 1+ Sulfur (S) 2– Li2S Aluminum (Al) 3+ Oxygen (O) 2– Al 2 O 3 

Beryllium (Be) 2+ Iodine (I) 1– BeI 2 

Calcium (Ca) 2+ Nitrogen (N) 3– Ca3N2 Sodium (Na) 1+ Bromine (Br) 1– NaBr 

Combination Compound Name Compound Name Chemical Family 

Al + Br aluminum bromide 1– 

Si + C2H3O2 silicon acetate 

Be + O beryllium oxide Lipase enzymes 

K + N potassium nitride Methanol alcohols 

2– 

Ba+CrO4 barium chromate Formic Acid organic acids 

Cs + F cesium fluoride Butane alkanes 

1+ 

NH3 +S ammonium sulfide Sucrose sugars 

Mg + Cl magnesium chloride Acetone ketones 

B + I boron iodide Acetic Acid organic acids 

2– 

Na+SO4 sodium sulfate Compound Name Chemical Family

Skill Sheet 14.1: Chemical Equations 

Part 1 answers: Part 2 answers: 

Reactants 

Hydrochloric acid 

HCl and 

Sodium hydroxide 

NaOH 

Calcium carbonate 

CaCO3 and 

Potassium iodide 

KI 

Aluminum 

fluoride 

AlF3 and 

Magnesium nitrate 

Mg(NO3) 2 

Products 

Water 

H2O and 

Sodium chloride 

NaCl 

Potassium 

carbonate 

K2CO3 Calcium iodide 

CaI2 Aluminum nitrate 

Al(NO3 ) 3 

and Magnesium 

fluoride 

MgF2 Unbalanced Chemical Equation 

HCl + NaOH → NaCl + H20 CaCO3 + KI → K2CO3 + CaI2 AlF3 + Mg(NO3 ) 2 → Al(NO3 ) 3 

+ MgF2 1. 4Al + 3O2 → 2Al2O3 2. CO + 3H2 → H2O + CH4 3. 2HgO → 2Hg + O2 4. CaCO3 → CaO + CO2 5. 3C + 2Fe2O3 → 4Fe + 3CO2 6. N2 + 3H2 → 2NH3 7. 2K+ 2H2O → 2KOH + H2 8. 4P + 5O2 → 2P2O5 9. Ba(OH) 2 + H2SO4 → 2H2O + BaSO4 10. CaF2 + H2SO4 → CaSO4 + 2HF 

11. 4KClO3 → 3KClO4 + KCl 

Skill Sheet 14.1: The Avogadro Number 


substance 

Atomic 

masses of 

elements 

(amu) 

Skill Sheet 14.1: Formula Mass 


1. First ion: Ca +2 ; Second ion: PO 4 3– 

2. Ca 3 (PO 4 ) 2 

3. 

No. of 

atoms of 

each 

element 

Skill Sheet 14.2: Classifying Reactions 

Formula 

mass 

(amu) 

Molar 

mass 

(g) 

Sr Sr 87.6 1 87.6 87.6 

Ne Ne 20.2 1 20.2 20.2 

Ca(OH) 2 Ca, O, H Ca, 40.1 

0, 16.0 

1 

2 

74.1 74.1 

H, 1.01 2 

NaCl Na, Cl Na, 23.0 1 58.5 58.5 

Cl, 35.5 1 

O3 O 16.0 3 48.0 48.0 

C6H12O C, H, O C, 12.0 

H, 1.01 

6 

12 

100 100 

O; 16.0 1 


Total mass 

(from periodic table) (number × atomic mass) 

Ca 3 40.08 120.24 

P 2 30.97 61.94 

O 8 16.00 128.00 

1. Synthesis. Two substances combine to make a new compound. 

2. Single displacement. Chlorine replaces potassium in the 

compound. 

3. Decomposition. A single compound is broken into two 

substances. 


substances. 

5. Combustion. A carbon compound reacts with oxygen to 

produce carbon dioxide and water. 

6. Double displacement. Two solutions are mixed and a solid is 

one of the products. 

7. Double displacement. Two solutions are mixed and a solid is 

one of the products. 

8. Single displacement. Sodium replaces calcium in the compound. 

Page 34 of 57 

Substance Molar mass 

(g) 

Mass of sample 

(g) 

Number of particles 

present 

MgCO3 84.32 12.75 9.10 × 1022 H2O 18.02 8.85 × 1029 296 × 1050 N2 28.02 3.30 × 10-14 7.1 × 108 Yb 173.04 0.00038 1.3 × 10 18 

Al2 (SO3 ) 3 294.17 4657 9.53 × 1024 K2CrO4 194.20 0.00074 0.23 × 10 19 

4. The formula mass for Ca3 (PO4 ) 2 : 120.24 g + 61.94 g + 

128.00 g = 310.18 g 


1. 

2. 

3. 

4. 

BaCl2 NaHCO3 Mg(OH) 2 

NH4NO3 formula mass: 

formula mass: 

formula mass: 

formula mass: 

208.23 

84.01 

58.33 

80.06 

5. Sr3(PO4) 2 formula mass: 452.80 


substances. 

10. Combustion. A carbon compound reacts with oxygen to 

produce carbon dioxide and water. 

11. This is a double displacement reaction because a solid forms 

from two solutions. 

12. A combustion reaction. 

13. Synthesis reaction because two substances form a single 

compound. 

14. The reaction is similar to a combustion reaction because a 

substance (hydrogen) reacts with oxygen and energy is 

produced. So is water. It is different because carbon is not 

involved in the reaction.

Skill Sheet 14.2: Predicting Chemical Equations 

1. Ca 

2. K 

3. Al 

4. Al + LiCl 

5. Ca + K 2 O 

Skill Sheet 14.2: Percent Yield 

1. 110.98 g 

2. 87.9% 

3. 104.3 g 

4. 63.55 g 

5. 88.0% 

6. 61.0 g 

7. 119.06 g 

Skill Sheet 14.4: Lise Meitner 

1. Ludwig Boltzmann was a pioneer of statistical mechanics. He 

used probability to describe how properties of atoms (like 

mass, charge, and structure) determine visible properties of 

matter (like viscosity and thermal conductivity). 

2. They discovered protactinium. Its atomic number is 91 and 

atomic mass is 231.03588. It has 20 isotopes. All are 

radioactive. 

3. The graphic at right 

illustrates fission 

(n = a neutron): 

4. Some topics students 

may research and 

describe include 

nuclear power 

plants, nuclear 

weapons, nuclear- 

Skill Sheet 14.4: Marie and Pierre Curie 

1. Sample answer: Marie (or Marya, as she was called) had a 

strong desire to learn and had completed all of the schooling 

available to young women in Poland. She was part of an 

illegal “underground university” that helped young women 

prepare for higher education. Perhaps her own thirst for 

knowledge fueled her empathy for the peasant children, who 

were also denied the right to an education. 

2. Marie Curie proposed that uranium rays were an intrinsic part 

of uranium atoms, which encouraged physicists to explore the 

possibility that atoms might have an internal structure. 

3. Marie and Pierre worked with uranium ores, separating them 

into individual chemicals. They discovered two substances 

that increased the conductivity of the air. They named the new 

substances polonium and radium. 

Skill Sheet 14.4: Rosalyn Yalow 

1. There are some striking similarities in the lives of Rosalyn 

Yalow and Marie Curie. As young women, both were 

outstanding math and science students. Even though Yalow 

was 54 years younger than Marie Curie, both faced limited 

higher education opportunities because they were women. 

Undaunted, each earned a doctorate degree in physics. Both 

Yalow and Curie’s research focused on radioactive materials. 

Curie’s work was at the forefront of discovery of how 

radiation works, while Yalow’s work was to develop a new 

application of radiation. Both women were particularly 

Page 35 of 57 

6. I 2 + KF 

7. Ca + K 2 S → 2K + CaS 

8. 3Mg + Fe 2 O 3 → 3MgO + 2Fe 

9. Li + NaCl → Na + LiCl 

8. 84% 

9. 107.2 g 

10. Experimental error, such as not measuring reactants or 

products carefully, spilling a reactant or product, or 

introducing a contaminant can affect the actual yield. Also, it 

may be impossible to measure every last bit of a reactant or 

product. 

powered submarines or aircraft carriers. 

5. Meitner’s honors included the Enrico Fermi award, and 

element 109, meitnerium, named in her honor. 

6. Students should include the following pieces of evidence in 

their letters: 

Meitner suggested tests to perform on the product of uranium 

bombardment. 

Meitner proved that splitting the uranium atom was 

energetically possible. 

Meitner explained how neutron bombardment caused the 

uranium nucleus to elongate and eventually split. 

4. Answers include nuclear physics, nuclear medicine, and 

radioactive dating. 

5. Marie Curie thought carefully about how to balance her 

scientific career and the needs of her children. When the 

children were young, Pierre’s father lived with the family and 

took care of the children while their parents were working. 

Marie spent a great deal of time finding schools that best fit 

the individual needs of her children and at one point set up an 

alternative school where she and several friends took turns 

tutoring their children. When her daughters were in their 

teens, Marie included them in her professional activities when 

possible. Irene, for example, helped her mother set up mobile 

x-ray units for wounded soldiers during the war. 

interested in the medical uses of radiation. Each was 

committed to using their scientific discoveries to promote 

humanitarian causes. Both women won Nobel Prizes for their 

work (Marie Curie won two!). 

2. RIA is a technique that uses radioactive molecules to measure 

tiny amounts of biological substances (like hormones) or 

certain drugs in blood or other body fluids. 

3. Using RIA, they showed that adult diabetics did not always 

lack insulin in their blood, and that, therefore, something

must be blocking their insulin’s normal action. They also 

studied the body’s immune system response to insulin 

injected into the bloodstream. 

4. The issue of patents in medical research remains a hotly 

debated issue in our society. Proponents of patents, especially 

for new drugs, claim that because very few new drugs make it 

through the extensive safety and effectiveness trials required 

for FDA approval, research costs are very high. Patents, they 

claim, are the only means of recouping these research costs. 

Skill Sheet 14.4: Chien-Shiung Wu 

1. Weak nuclear force: One of the fundamental forces in the 

atom that governs certain processes of radioactive decay. It is 

weaker than both the electric force and the strong nuclear 

force. If you leave a solitary neutron outside the nucleus, the 

weak force eventually causes it to break into a proton and an 

electron. The weak force does not play an important role in a 

stable atom, but comes into action in certain cases when 

atoms break apart. 

Beta decay: a radioactive transformation in which a neutron 

splits into a proton and an electron. The electron is emitted as 

a beta particle and the proton stays in the nucleus, increasing 

the atomic number by one. 

Isotope: Forms of the same element that have different 

numbers of neutrons and different mass numbers. 

2. When Enrico Fermi was having difficulty with a fission 

experiment, he turned to Wu for assistance. She recognized 

the cause of the problem: a rare gas she had studied in 

graduate school. Because she was familiar with the behavior 

of the gas she was able to help Fermi get on with his work. 

3. The law of conservation of parity stated that in nuclear 

reactions, there should be no favoring of left or right. In beta 

decay, for example, electrons should be ejected to the left and 

to the right in equal numbers. 

4. Cobalt-60 has 27 protons and 33 neutrons. There is only one 

stable isotope of cobalt, cobalt-59. 

5. Wu cooled cobalt-60 to less than one degree above absolute 

zero, then placed the material in a strong magnetic field so 

that all the cobalt nuclei lined up and spun along the same 

axis. As the radioactive cobalt broke down and gave off 

Skill Sheet 14.4: Radioactivity 

1. In the answers below, “a” is alpha decay and “b” is beta 

decay. 

a. Answers are: 

238 

92 a→ b→ b→ a→ a→ 

U 

234 

90 Th 

234 

91 Pa 234 

92 U 230 

90 Th 

226 

88 a→ a→ a→ b→ b→ 

a→ b→ b→ a→ 

b. Answers are: 

b→ a→ a→ b→ a→ 

Ra 

222 

86 Rn 218 

84 Po 214 

82 Pb 214 

83 Bi 

214 

84 Po 

210 

82 Pb 210 

83 Bi 210 

84 Po 206 

82 Pb 

240 

94 Pu 

240 

95 Am 

236 

93 Np 232 

91 Pa 232 

92 U 

228 

90 Bi 

212 

83 Bi 

224 

88 Ra 

a→ b→ a→ a→ a→ 

212 

84 Po 

224 

89 Ac 

208 

82 Pb 

b→ a→ b→ 

220 

87 Fr 

Skill Sheet 15.2: Svante Arrhenius 

208 

83 Bi 

216 

85 At 

1. Arrhenius studied what happens when electricity is passed 

through solutions. He proposed that molecules in solutions 

could break up into electrically charged fragments called ions. 

Page 36 of 57 

On the other side of the issue, critics say that the profit motive 

drives research into certain types of medicines—tending to be 

drugs for chronic illnesses, so that patients will take the drugs 

for a long time. Research into drugs (like new antibiotics) that 

are generally taken only for a short period of time tends to be 

less of a priority. You may wish to have students research the 

pros and cons of the patent system and write a position paper 

or hold a class discussion or debate on the topic. 

electrons, Wu observed that far more electrons flew off in the 

direction opposite the spin of the nuclei. She proved that the 

law of conservation of parity does not hold true in all cases. 

6. Margaret Burbridge, professor of astronomy, UCLA-awarded 

the National Medal of Science in the physical sciences in 

1983. Citation: “For leadership in observational astronomy. 

Her spectroscopic investigations have provided crucial 

information about the chemical composition of stars and the 

nature of quasi-stellar objects.” 

Vera C. Rubin, staff member, astronomy, Carnegie Institute of 

Washington-awarded the National Medal of Science in the 

physical sciences in 1993. Citation: “For her pioneering 

research programs in observational cosmology which 

demonstrated that much of the matter in the universe is dark 

and for significant contributions to the realization that the 

universe is more complex and more mysterious than had been 

imagined.” 

7. Answers may vary. Some interesting questions to research 

include: 

What are some other experiments or projects Wu undertook 

during the course of her career? 

Did she ever return to her home country? 

What advice would she give young people who wish to 

become scientists? 

8. Unfortunately, the contributions of women to science were 

often overlooked. When the prize was awarded to Lee and 

Yang, playwright Clare Booth Luce commented, “When Dr. 

Wu knocked out that principle of parity, she established the 

principle of parity between men and women.” 


a. During 11 minutes, fluorine-18 would experience 6 halflives. 

b. 0.16 gram would be left after 11 minutes (660 seconds). 

3. The amount after 28,650 years would be 0.0313m (or 1/32m) 

where m is the mass of the sample. 

4. For one-fourth of the original mass to be left, there must have 

been time for two half-lives. Therefore, the half-life for this 

radioactive isotope is 9 months. 


a. 0.8 W/m 2 

b. 3.6 × 10 13 reactions per second 

2. Arrhenius had always been a strong student. However, his 

doctoral thesis was not well understood and he was given a

arely passing grade. This made it difficult for him to find 

work in a university after graduation. 

3. Arrhenius was interested in physical chemistry, biology, 

astronomy, and meteorology. 

4. Arrhenius suggested that life may have spread from one part 

of the universe to another when living spores from one planet 

escaped their atmosphere and were then pushed along by 

Skill Sheet 16.1: Open and Closed Circuits 


a. A, B 

b. A, C, D 

c. A, B, C 

d. no current 

e. A, B, D 

f. B, C, D 

g. A, C 

h. A 

i. A 

j. no current 


a. A, B, C, D, E 

b. A, B, C, D, E, F, G 

c. A, B, C, D, E 

d. A, B, C, D, F, G 

e. A, B, C 

f. B, C, D, E, F, G 

g. no current 

h. B, C, D, F, G 

i. A, B, C, D, F, G 

j. A, B, C 

k. A, B, C, D, E 

l. B, C 

m. A, B, C 

Skill Sheet 16.1: Benjamin Franklin 

1. Franklin learned through reading, writing, discussing, and 

experimenting. 

2. Franklin’s hypothesis was that lightning is an example of a 

large-scale discharge of static electricity. 

3. Franklin’s reported results were that the loose threads of the 

hemp stood up and that touching the key resulted in a static 

electric shock. He concluded that the results were consistent 

with other demonstrations of static electricity; therefore, 

lightning was a large-scale example of the same phenomenon. 

4. If the kite had been struck by lightning, the amount of charge 

coming down the hemp string would most likely have 

electrocuted Franklin. 

Skill Sheet 16.2: Using an Electrical Meter 

Page 37 of 57 

radiation pressure to other places in the universe until they 

landed on another hospitable planet. 

5. Arrhenius was one of the first to explain the role of 

“greenhouse gases” in warming the surface of the planet. He 

also proposed that humans could change Earth’s average 

temperature by adding carbon dioxide to the atmosphere. 

n. no current 

o. B, C 

3. Diagrams: 

4. diagram #1: 4 paths; diagram #2: 8 paths 

5. Student drawings will vary. If time permits, allow students to 

build and test their circuits 

5. The diagram shows 

electrons moving from 

the glass rod to the silk 

so that the silk becomes 

negatively charged and 

the glass becomes 

positively charged. 

6. A lightning rod is a 

metal rod attached to the 

roof of a building. A 

thick cable stretches 

from the rod to a metal 

1. Sample diagram: 2. First battery: 1.553 volts; second battery: 1.557 volts 

3. First bulb: 1.514 volts; second bulb: 1.586 volts 

4. 3.113 volts 

5. 3.108 volts 

6. The two voltages are approximately equal. 

7. post #1: 0.0980 amps 

post #2: 0.0981 amps 

post #3: 0.0978 amps 

post #4: 0.0980 amps 

post #5: 0.0980 amps

8. The current is approximately the same at all points. 

9. First bulb: 15.4 ohms; second bulb: 16.2 ohms 

10. Measuring resistance: First, set the meter dial to measure 

resistance. Remove the bulb from its holder. Then place one 

lead on the side of the metal portion of the light bulb (where 

the bulb is threaded to fit into the socket). Place the other lead 

on the “bump” at the base of the light bulb. The meter will 

display the bulb’s resistance. 

Measuring voltage: First, set the meter dial to measure DC 

voltage. Locate the device (battery, bulb, etc.) that you wish 

to measure the voltage across. Then place one meter lead on 

Skill Sheet 16.3: Voltage, Current, and Resistance 

Reading section answers: 

1. A battery with a larger voltage can create a greater energy 

difference. A 9-volt battery gives a greater “push” to the 

charges and creates a larger current. 

2. You could increase the number of batteries, which would 

increase the total voltage in the circuit. You could replace the 

light bulb with a bulb of lower resistance. You could also use 

thicker wires, shorter wires, or wires made from a material 

with a higher conductivity. These changes to the wires would 

decrease the total amount of resistance in the circuit. 

3. If the circuit used a 9-volt battery, you could try replacing it 

with five (or less than five) 1.5-volt batteries to lower the 

voltage in the circuit. You could replace the bulb with a bulb 

of higher resistance. Or, you could use thinner wires, longer 

wires, or wires made from a material with a lower 

conductivity. These changes to the wires would increase the 

Skill Sheet 16.3: Ohm’s Law 

1. 3 amps 

2. 0.75 amp 

3. 0.5 amp 

4. 1 amp 

5. 120 volts 

6. 8 volts 

7. 50 volts 

8. 12 ohms 

9. 240 ohms 

10. 1.5 ohms 

11. 3 ohms 


a. Circuit A: 6 V; Circuit B: 12 V 

b. Circuit A: 1 A; Circuit B: 2 A 

c. Circuit A: 0.5 A; Circuit B: 1 A 

Skill Sheet 16.4: Series Circuits 


a. 6 volts c. 3 amps 

b. 2 ohms d. 3 volts 

c. Diagram: 

Page 38 of 57 

one of the posts next to the device. Put the other meter lead on 

the post on the other side of the device. The meter will display 

the device’s voltage. If it shows a negative voltage, switch the 

two leads. 

Measuring current: First, set the meter to measure DC current. 

Then break the circuit at the location where you wish to 

measure the current. Connect one of the meter leads at one 

side of the break. Connect the other lead at the other side of 

the break. The meter will display the current. If it shows a 

negative current, switch the two leads. 

total resistance in the circuit. To stop the current completely, 

you could simply open the switch. 

4. You could simply cut each piece of wire in the circuit as short 

as possible. A shorter wire has less resistance than a longer 

wire. To make a more significant decrease in resistance, you 

would need to replace the wire with a thicker gauge wire or a 

wire made from a material with greater conductivity. 

5. Ohm’s law states that, in a circuit, the amount of current is 

directly related to voltage, and inversely related to the 

resistance in the circuit. 

Problem section answers: 

1. 1.5 amps 

2. 0.75 amps 

3. 50 volts 

4. 12 ohms 

d. It is brighter in circuit B because there is a greater voltage 

and greater current (and more power is consumed since 

power equals current times voltage). 

13. The current becomes 4 times as great. 

14. If resistance increases, the current decreases. The two are 

inversely proportional. 

15. If voltage increases, current increases. The two are directly 

proportional. 

16. Remove one of the light bulbs. This decreases the resistance 

and increases the current. 

17. Remove one of the batteries. This decreases the voltage and 

decreases the current. 


a. 2 batteries and a 3 ohm bulb (or 4 batteries and all 3 bulbs) 

b. 4 batteries and a 3 ohm bulb 

c. 2 batteries and a 1 ohm bulb (or 4 batteries and a 2 ohm 

bulb) 

d. 4 batteries and a 1 ohm bulb 


a. 6 volts c. 2 amps 

b. 3 ohms d. 2 volts 

c. Diagram:

3. The current decreases because the resistance increases. 

4. The brightness decreases because the voltage across each 

bulb decreases and the current decreases. Since power equals 

voltage times current, the power consumed also decreases. 


a. 3 ohms 

b. 2 amps 

c. 1 ohm bulb: 2 volts; 2 ohm bulb: 4 volts 


a. 12 volts 

b. 4 ohms 

c. 3 amps 

d. 6 volts 

e. Diagram: 

Skill Sheet 16.4: Parallel Circuits 

Practice set 1: 


a. 12 volts 

b. 6 amps 

c. 12 amps 

d. 1 ohm 


a. 12 volts 

b. 4 amps 

c. 8 amps 

d. 1.5 ohms 


a. 12 volts 

b. 2 ohm branch: 6 amps; 3 ohm branch: 4 amps 

c. 10 amps 

d. 1.2 ohms 

Skill Sheet 16.4: Thomas Edison 

1. Edison’s education included one-on-one tutoring from his 

mother, reading lots of books, and performing experiments in 

laboratories that he set up. 

2. Edison learned that in order to sell an invention, not only does 

it have to be a technical success, it also has to be something 

that people want to buy. 

3. Edison’s research facility at Menlo Park had workshops, 

laboratories, offices, and a library. Edison hired a team of 

assistants with various specialties to work there. 

Page 39 of 57 


a. 2 ohms 

b. 1 volt 

c. Diagram: 


a. 6 ohms 

b. 1.5 amps 

c. 2 ohm resistor: 3 volts; 3 ohm resistor: 4.5 volts; 1 ohm 

resistor: 1.5 volt 

d. The sum is 9 volts, the same as the battery voltage. 


a. Diagram A: 0.5 amps; Diagram B: 1.0 amps 

b. Diagram A: 0.25 amps; Diagram B: 0.5 amps 

c. The amount of current increases. 


a. 9 volts 

b. 2 ohm branch: 4.5 amps; 3 ohm branch: 3 amps; 1 ohm 

branch: 9 amps 

c. 16.5 amps 

Practice set 2: 


a. 4 ohms 

b. 6 ohms 

c. 2.67 ohms 

d. 2.4 ohms 


a. 2.67 ohms 

b. 1.2 ohms 

c. 0.545 ohms 

4. The tin foil phonograph and a practical, safe, and affordable 

incandescent light were developed at Menlo Park. 

5. Edison’s invention process was to brainstorm as many ideas 

as possible, try everything that seems even remotely 

workable, record everything, and use failed experiments to 

redirect the project. 

6. Edison was not easily discouraged by failure. Instead, he saw 

failed projects as providing useful information to narrow 

down the possibilities of what does work.

7. Students can find information about Edison’s tin foil 

phonograph using the Internet. Here’s a summary of how it 

worked: 

Edison set up a membrane that vibrated when exposed to 

sound waves. The membrane (called a diaphragm) had an 

embossing needle attached. When someone spoke, the 

diaphragm would vibrate and the embossing needle would 

make indentations on tin foil wrapped around a metal 

cylinder. The cylinder was turned by a hand-crank at around 

Skill Sheet 16.4: George Westinghouse 

1. Westinghouse first developed his talents as an inventor in his 

father’s agricultural machine shop. 

2. Westinghouse enabled trains to travel more safely at higher 

speeds in two ways: He invented an air brake which allowed 

the engineer to stop all the cars at once, and he developed 

signaling and switching systems which reduced the likelihood 

of collisions. 

3. Westinghouse promoted alternating current because it could 

be transmitted over longer distances. 

4. Westinghouse demonstrated the potential of alternating 

current by lighting the streets of Philadelphia and then the 

entire Chicago World’s Fair using this technology. 

5. Direct current occurs when charge flows in one direction. 

Batteries provide direct current. Alternating current, in 

contrast, switches directions. Household circuits in the United 

States run on alternating current that reverses direction 60 

times each second. The diagrams below compare direct and 

alternating current. 

Skill Sheet 16.4: Lewis Latimer 

1. Lewis Latimer did not attend college, but learned how to be a 

draftsman by studying the drawings of draftsmen while 

working as an office boy for a patent law firm. He was selfmotivated 

and used any available books and tools to learn the 

skills needed to become an outstanding draftsman. He was 

also a self-taught electrical engineer. He learned all that he 

could about electricity while working for Hiram Maxim at 

U.S. Electric Lighting. 

2. Latimer invented the following: 

Mechanical improvements for railroad train water closets 

(also known as toilets) 

Carbon filaments to replace paper filaments in light bulbs 

An improved manufacturing process for carbon filaments 

An early version of the air conditioner 

A locking rack for hats, coats, and umbrellas 

A book support 

His most important inventions are the development of carbon 

fibers and improved manufacturing process to produce those 

filaments. The light bulb invented by Thomas Edison used a 

paper filament. As a result, it had a very short life span. With 

carbon filaments, light bulbs lasted longer, were more 

Page 40 of 57 

60 revolutions per minute. There was a second diaphragmand-needle 

apparatus for playback. When the needle followed 

the “tracks” made in the tin foil, it made the diaphragm 

vibrate which reproduced the recorded sounds. 

8. Answers will vary. Some of Edison’s interesting inventions 

include paraffin paper, an “electric pen” (the forerunner of the 

mimeograph machine) a carbon rheostat, a fluoroscope, and 

sockets, switches, and insulating tape. 

6. Westing house used hydroelectric generators at Niagara 

Falls to provide electricity to the city of Buffalo. 

7. Westinghouse’s Manhattan elevated trains were electrical 

powered using alternating current. 

8. Answers may vary. Some of Westinghouse’s other 

inventions include: Apparatus for safe transmission of 

natural gas, the transformer, a machine that placed 

derailed train cars back on the tracks, and a compressed 

air spring. 

affordable, and could be used in a variety of ways. Latimer 

improved the technology so that light bulbs would become 

commonplace in both industry and homes. 

3. A “Renaissance man” is a scholar with a depth of knowledge 

in a variety of areas. During the Renaissance, there were men 

who were accomplished in multiple disciplines including 

math, engineering, art, and music. Leonardo da Vinci was one 

of the great Renaissance men. Lewis Latimer can be called a 

Renaissance man because he, too, excelled in a variety of 

areas including science, literature, music, and art. 

4. Two of Latimer’s poems were titled Friends and Ebon Venus. 

5. The Edison Pioneers first met on February 11, 1918. This was 

Thomas Edison’s 71st birthday. 

Excerpt from obituary: 

“He was of the colored race, the only one in our organization, 

and was one of those to respond to the initial call that led to 

the formation of the Edison Pioneers, January 24, 1918. 

Broadmindedness, versatility in the accomplishment of things 

intellectual and cultural, a linguist, a devoted husband and 

father, all were characteristic of him, and his genial presence 

will be missed from our gatherings.”

Skill Sheet 17.1: Magnetic Earth 

1. Students learn in Chapter 17 that Earth’s magnetic field 

comes from its core. For those who desire a more detailed 

explanation, scientists believe that the motion of molten 

metals in Earth’s outer core create its magnetic field. 

2. Seven percent of 0.5 gauss is 0.035 gauss. In 100 years, 

Earth’s strength could be 0.465 gauss. 

3. Student answers will vary but may include responses such as: 

devices that depend on magnets would work differently or not 

at all. Earth science experts tell us that the poles could reverse 

within the next 2,000 years. During a reversal, the field would 

not completely disappear. The main magnetic field that we 

use for navigation would be replaced by several smaller fields 

with poles in different locations. 

4. Rock provides a good record because as the rock is made, 

atoms in the rock align with the magnetic field of Earth. 

(Actually, oceanic rock is made of a substance called 

magnetite!) Rock that was made 750,000 years ago would 

have a north-south orientation that is exactly opposite the 

north-south orientation of rock that is made today. Therefore, 

we can use the north-south orientation of bands of rock on the 

sea floor to understand how many times the poles have 

reversed over geologic time. 

5. NOTE: In many references, magnetic south pole is referred to 

as “magnetic north pole” because it is located at the 

geographic north pole. This terminology can be confusing to 

students who know that opposite poles attract. The north pole 

of a compass needle is in fact the north end of a bar magnet. 

This is why we think it is best to use the term magnetic south 

pole as the point to which the north end of a compass needle 

is attracted. For more information about Earth’s magnetism 

see http://www.ngdc.noaa.gov/. 

Answers are: 

a. Both the magnetic south pole and geographic north are 

located near the Arctic. 

Skill Sheet 17.2: Maglev Train Model Project 

Students build a model to complete this skill sheet. No written 

responses are required. 

Skill Sheet 17.4: Michael Faraday 

1. Faraday took careful notes during lectures given by Davy, 

then bound his notes and sent them to Davy along with a 

request for a job. Faraday had little formal training in science, 

so this was a means of proving his capabilities. 

2. Benzene is used in cleaning solvents, herbicides, insecticides, 

and varnishes. Note: Benzene is a known carcinogen and 

highly flammable. Safety precaution must be taken whenever 

it is used. 

3. Electromagnetic induction is the use of a moving magnet to 

create an electric current. 

4. Sample answer: When light is polarized (vibrating in one 

plane), a strong magnetic field can change the orientation of 

that plane. 

5. Faraday instituted the Friday Evening Discourses and the 

Christmas Lectures for Children, which gave non-scientists 

Skill Sheet 17.4: Transformers 

1. 25 turns 

2. 230 volts 

3. 220 volts 

4. 100 volts 

Page 41 of 57 

b. The magnetic south pole is about 1,000 kilometers from 

the geographic north pole. 

c. Magnetic south pole is the point on Earth’s surface that 

corresponds to Earth’s south pole if you think of Earth’s 

core as a bar magnet. Magnetic south pole is located at a 

distance from the geographic north pole or ‘true north.’ 

True north is a point on Earth’s surface that we call north. 

‘True north’ and ‘true south’ follow Earth’s axis. If we 

want to go north, we need to head toward Earth’s 

geographic north. The tool we use to head north, however, 

points us toward the magnetic south pole. We use 

magnetic declination to correct for this. 

6. A compass needle is a bar magnet. Its north pole is attracted 

to Earth’s magnetic south pole (if you consider the interior of 

Earth is like a bar magnet). Using magnetism, we can find our 

way using north as a reference point. However, using 

magnetism actually points us a bit off course because the 

magnetic south pole is not located at the same position as true 

north. 


a. Example problem: northeast. 

b. south 

c. west 

d. east 

e. southeast 

f. northwest 

8. If you didn’t correct your compass for magnetic declination, 

you would be off course and possibly get lost. 

9. Yes, magnetic declination equals zero on Earth’s surface 

along a line that goes from New Orleans through the eastern 

edge of Minnesota up through Churchill, Canada. However, 

the location of the zero-degree line is always changing. For 

more information about Earth’s magnetic declination and 

magnetism, see http://www.ngdc.noaa.gov/. 

the opportunity to learn about the scientific community and 

about recent advances in science. 

6. The electric motor, invented by Faraday, is used in all sorts of 

household appliances including electric fans, hair dryers, food 

processors, and vacuum cleaners. Electromagnetic induction 

is used by local power plants to generate the electricity that is 

used every day. 

7. Faraday had a reputation as an engaging speaker who used 

exciting demonstrations to catch his audience’s interest. He 

had a knack for communicating scientific knowledge in terms 

that non-scientists understood. It also would be interesting to 

see who else might be in attendance at the lecture! 

8. Iron filings are available from many science supply catalogs. 

Place some iron filings on a piece of clear plastic (such as an 

overhead transparency). Place the plastic over a magnet to 

observe the field lines. 

5. 440 turns 

6. 131 turns

Skill Sheet 17.4: Electrical Power 


a. 5 kW 

b. 10 kWh 

c. $1.50 


a. 300 minutes 

b. 5 hours 

c. 1.2 kW 

d. 6 kW 

e. $0.90 

3. 960 W 

4. 24 W 


a. 60 W 

b. 0.06 kW 

c. 525.6 kWh 

d. $78.84 

6. 0.625 A 


a. 3 V 

b. 1 A 

c. 3 W 

Skill Sheet 18.1: Andrew Douglass 

1. Douglass originally started as an astronomer. He helped to 

set-up observatories and also studied Mars with Percival 

Lowell. He noticed a possible relationship between sunspot 

cycles and the climate and wished to study this further. He 

noted that tree rings held information about weather patterns 

and hoped he could find a link between periods of drought 

and sunspot activity. This marked his move away from 

astronomy and toward tree ring analysis. 

2. Douglass created the science of dendrochronology or tree ring 

dating. He specifically developed cross-dating as a technique 

to match tree ring samples with ancient ruins. 

3. Douglass, in 1929, was able to date with accuracy Native 

American ruins in Arizona. He studied pine tree rings dating 

back to the time of Native American dwellings. He matched 

wooden beam samples against pine tree rings to determine a 

Skill Sheet 18.2: Relative Dating 

1. A thunderstorm began. A child ran through a mud puddle 

leaving footprints. Hail began to fall. Finally, the mud puddle 

dried and cracked. 

2. One April afternoon, a thunderstorm began. A child was 

outside playing. When the rain began to fall hard, the child 

ran home. Her footprints were left in a mud puddle. 

Fortunately, she made it home just in time because small 

hailstones suddenly began to fall. The hailstorm lasted for a 

few minutes and then the clouds cleared. The next morning 

was bright and sunny. The mud puddle dried and then cracked 

in many places. 

3. C 

4. E (This is the term that will be new to students.) 

5. A 

6. F 

7. B 

8. D 

9. There is no matching picture for this concept. The name of 

this concept is faunal succession. 

Page 42 of 57 


a. 24 ohms 

b. 600 W 

c. 0.6 kW 


a. 20.5 A 

b. 10.8 ohms 

c. 18 kWh 

d. $140.40 


a. 6 ohms 

b. 2 A 

c. 12 W 

d. 24 W 


a. 12 V 

b. 4 A 

c. 48 W 

d. 8 A 

e. 96 W 

precise date for the ancient ruins. This cross-dating technique 

provided a tool for all archaeologists to date prehistoric 

remains and ruins. 

4. The second asteroid is called Minor Planet or Asteroid 

(15420) Aedouglass. 

5. The Boyden Observatory is now located in Bloemfontein, 

South Africa. 

6. The Spacewatch Project is located at the University of 

Arizona’s Lunar and Planetary Laboratory. Scientists at 

Spacewatch study and explore small objects in the solar 

system including asteroids and comets. The Project was 

founded by Professor Tom Gehrels and Dr. Robert S. 

McMillan in 1980. 

10. The rock bodies formed in this order: H, G, F, D, C, B, E, and A. 

11. The fault formed after layer F and before both layer D and the 

intrusion. 

12. The stream formed after layer A. Like an intrusion, the stream 

cut across the rock bodies. 

Extension 

13. The set of clues 

includes three layers 

of colored sand in a 

clear tank. The layers 

were made while a 

small pencil was held 

upright. The sand 

filled in around the 

pencil. After the layers 

were created, a 

second, longer pencil 

was pushed through 

the layers.

14. The concepts of original horizontality and lateral continuity 

are demonstrated here. Pencil E represents cross-cutting 

relationships. Pencil D represents the idea of inclusions. 

Skill Sheet 18.2: Nicolas Steno 

1. Steno is responsible for the following three principles of 

geology: 

The principle of superposition states that layers of 

sedimentary rock settle on top of each other. The oldest 

layers are at the bottom and the younger layers are on top. 

The bottom layers are formed first with younger layers 

sitting above. Geologists use this principle to determine the 

relative ages of layers. 

The principle of original horizontality states that 

sedimentary rock layers form horizontally. 

The principle of lateral continuity states that rock layers 

spread out until they reach something that stops this 

spreading. The layers will continue to move out in all 

directions horizontally until they are stopped. 

2. People did not understand how fossils formed and what 

fossils truly were. Common misconceptions included the 

following: fossils grew inside rocks, fossils fell from the sky, 

and fossils fell from the moon. People did not consider 

extinction or have an understanding of geological principles 

to understand fossils and fossil formation. 

3. Steno identified tongue stones as ancient shark teeth. He 

understood that particles settled in sediment. The shark teeth 

had settled into soft sediment that eventually hardened. 

Sharks had once lived in the mountains that at one time had 

been covered by the sea. Shark teeth became buried in mud 

and rock layers formed around the teeth. These layers became 

buried under new layers of rock 

4. As an anatomist, Steno developed keen observation skills. He 

was comfortable examining something in depth and trying to 

Skill Sheet 18.3: The Rock Cycle 

Skill Sheet 19.1: Earth’s Interior 

A. Crust 

B. Upper mantle 

C. Asethenosphere 

D. Lower mantle 

E. Outer core 

F. Inner core 

Page 43 of 57 

15. The order of the events is D, A, B, C, and E. My classmates 

successfully figured out the correct order of the events. 

understand how something worked. He was not merely 

satisfied with viewing something. He liked to take things 

apart. His medical background and work in anatomy made 

him a hands-on researcher. He took his observation and 

interest in understanding structure and applied those skills to 

geology. Unlike many of his counterparts who simply read 

scholarly works, Steno was a true field scientist. He traveled, 

observed, and touched. 

5. Answers will vary. Students might suggest observations they 

have made in a science lab, at the beach, or on a field trip. In 

general, observation often teaches us that things are not what 

they may initially appear. Observation means paying attention 

to the details, even if minute or mundane. 

6. A goldsmith is a metalworker who often makes jewelry. A 

goldsmith will solder, file, and polish. A goldsmith does not 

work only with gold, but will handle a variety of metals. Most 

work by a goldsmith is done by hand. Steno’s father’s 

goldsmith shop was a laboratory providing him with the 

opportunity to use his hands to handle various tools and 

materials. 

Alchemy is the early ancestor of chemistry. This ancient form 

of chemistry included herbs and metals. Alchemists often 

looked for cures for illnesses. Goldsmith work and alchemy 

both took place in a laboratory-like setting providing Steno 

exposure to scientific concepts and materials. Alchemists 

liked to experiment and tried to understand the world around 

them. Steno used observation and his hands throughout his 

career as a scientist to make sense of the world around him.

Skill Sheet 19.1: Charles Richter 


theoretical physics—a branch of physics that attempts to 

understand the world by making a model of reality, used 

for rationalizing, explaining, and predicting physical 

phenomena through a “physical theory.” 

seismology—The study of earthquakes and of the 

structure of the Earth by natural and artificial seismic 

waves. 

seismograms—A written record of an earthquake, 

recorded by a seismograph. 

magnitude—the property of relative size or extent 

(whether large or small) 

seismographs—An instrument for automatically detecting 

and recording the intensity, direction, and duration of a 

movement of the ground, especially of an earthquake. 

2. Sample answer: I would feel proud that a leader in the field 

considered me above anyone else. It would be disappointing 

to lose the opportunity to work with Dr. Millikan, but if he 

considered me ready for the job, maybe he felt I had learned 

all I could and was ready to move on. 

3. Richter responded by taking on routine tasks and making 

something extraordinary out of something ordinary. 

4. Dr. Beno Gutenburg 

Skill Sheet 19.1: Jules Verne 

1. Verne’s novels offered people an opportunity to go on 

voyages into unknown realms of the world, and even space. 

Tales like these are still popular today, but during Verne’s 

time, fewer people had the opportunity to travel. Verne’s 

novels pulled readers away from their everyday life and 

allowed their imaginations to consider futuristic inventions 

and machines that were far removed from life in the 

nineteenth century. 

2. From Earth to the Moon, 20,000 Leagues Under the Sea, 

Journey to the Center of the Earth, Around the World in 80 

Days, and The Mysterious Island have all been made into 

movies several times. Around the World in 80 Days won five 

academy awards in 1956 including best picture and best 

cinematography. 

3. The bar exam is a written test that must be passed in order to 

qualify a person to practice law. 

Skill Sheet 19.2: Alfred Wegener 

1. He developed an interest in Greenland when he was a young 

boy. As an adult scientist, he went there on several scientific 

expeditions to study the movement of air masses over the 

polar ice cap. He studied the movement of air masses long 

before the common acceptance of the jet stream. He died 

there during a blizzard on one of his expeditions just a few 

days after his fiftieth birthday. 

2. He and his brother set the world record for staying aloft in a 

hot air balloon for the longest period of time, 52 hours. 

3. Wegener studied and used several different fields of science 

in his work. His main areas of expertise were astronomy and 

meteorology, however, he also explored paleontology 

(fossils), geology, and climatology as he gathered evidence 

for his drifting continent theory. 

4. Fossils of the small reptile were found only on the eastern 

coast of Brazil and the western coast of Africa. Since there 

was no way that the reptile could have crossed the Atlantic 

Ocean, Wegener figured that those two continents must have 

been connected when that reptile was alive. 

Page 44 of 57 

5. Answers will vary. Correct answers include: 

a. Mercalli scale 

b. Moment magnitude scale 

c. JMA scale (Japanese Meteorological Agency) 

d. MSK scale (Medvedev, Sponheuer and Karnik) 

e. European Macroseismic scale 

f. Rossi-Forel scale 

g. Omori scale 

6. Some scales measure intensity (like the Mercalli scale), while 

others measure magnitude (like the Richter scale). Intensity 

scales measure how strongly a quake affects a specific place, 

while magnitude scales indicate how much total energy a 

quake expends. Also, many times different countries have 

different building codes or standards of construction. Some of 

the scales used to measure earthquakes are based on 

traditional construction materials and techniques, which can 

vary around the world. These scales may be used to define the 

quake resistant construction guidelines adopted by different 

countries or regions with different occurrences of 

earthquakes. 

7. Seismograph and seismometer are usually interchangeable, as 

they both describe devices designed to do the same thing. 

Seismometer seems to be the more modern term. 

4. Victor-Marie Hugo (February 26, 1802–May 22, 1885) is 

recognized as the most influential French Romantic writer of the 

19th century and is often identified as the greatest French poet. 

Two of his best known works are Les Misérables and The 

Hunchback of Notre-Dame. Verne must have been inspired to 

meet the most famous and well-respected author of his time. 

5. Airplanes, movies, guided missiles, submarines, the electric 

chair, air conditioning, the fax machine, gas-powered cars, 

and an elevated mass transit system are among his best 

known. One of his most eerily true-to-life ideas appears in 

both From Earth to the Moon (1865) and All Around the 

Moon (1870). In these stories an aluminum craft launched 

from central Florida achieves a speed of 24,500 miles per 

hour, circles the moon and splashes down in the Pacific. A 

century later Apollo 8, made of aluminum and traveling at 

24,500 miles an hour, took off from central Florida. It circled 

the moon and splashed down in the Pacific. 

5. Coal can only be formed under certain conditions. It can be 

formed only from plants that grow in warm, wet climates. Those 

type of plants could not grow in either England or Antarctica 

today. That means that at some time, England and Antarctica 

must have been located somewhere around the equator where 

those type of plants could survive, and they must have moved 

away from the equator to their present locations. 


7. Wegener was a relatively unknown scientist at the time, and 

geology wasn’t even his field of expertise, yet he was proposing 

a theory that went against everything that scientists at the time 

believed about geology. The most famous scientists alive at that 

time attacked him viciously and called his theory utter rot! Also, 

even though he had gathered what appeared to be a lot of 

evidence to show that the continents had indeed moved over 

millions of years, he could never explain how or why that 

happened. He could never explain what driving force could be 

powerful enough to move continents. 

8. Answers will vary.

Skill Sheet 19.2: Harry Hess 

1. Hess used his time in the Navy to further his geological 

research. Between battles, Hess and his crew gathered data 

about the structure of the ocean floor using the ship’s 

sounding equipment. They recorded thousands of miles worth 

of depth recordings. 

2. While in the Navy, Hess measured the deepest point of the 

ocean ever recorded-nearly 7 miles deep. He also discovered 

hundreds of flat-topped mountains lining the Pacific Ocean 

floor. He named these unusual mountains “guyouts”. 

3. Hess explained that sea floor spreading occurs when molten 

rock (or magma) oozes up from inside the Earth along the 

mid-oceanic ridges. This magma creates new sea floor that 

spreads away from the ridge and then sinks into the deep 

oceanic trenches where it is destroyed. 

4. Hess explained that the ocean floor is continually being 

recycled and that sediment has been accumulating for no 

Skill Sheet 19.2: John Tuzo Wilson 

1. Wilson’s adventurous parents helped to expand Canada’s 

frontiers. Wilson’s mother, Henrietta Tuzo, was a famous 

mountaineer who had Mount Tuzo in western Canada named 

in her honor. Wilson’s father, also named John, helped plan 

the Canadian Arctic Expedition of 1913 to 1918. He also 

helped develop airfields throughout Canada. 

2. Wilson is sometimes called an adventurous scholar because 

he enjoyed traveling to unusual locations. He became the first 

person to scale Mount Hague in Montana. Wilson also led an 

expedition called Exercise Musk-Ox in which ten army 

vehicles traveled 3,400 miles through the Canadian Arctic. 

While a professor, Wilson mapped glaciers in Northern 

Canada and became the second Canadian to fly over the 

North Pole during his search for unknown Arctic islands. 

3. Volcanic islands, like the Hawaiian Islands, are found 

thousands of kilometers away from plate boundaries. In 1963, 

Wilson published a paper that explained how plates move 

Skill Sheet 19.3: Earth’s Largest Plates 

A. Pacific Plate 

B. North American Plate 

C. Eurasian Plate 

Skill Sheet 19.4: Continental U.S. Geology 


Skill Sheet 20.1: Finding an Earthquake Epicenter 

Practice 1: 

Table 1 answers: 

Station 

name 

Arrival time 

difference between 

P- and S-waves 

Distance to 

epicenter in 

kilometers 

1 15 seconds 130 km 1.3 cm 



Scale distance 

to epicenter in 

centimeters 

Page 45 of 57 

more than 300 million years. This is the amount of time 

needed for the ocean floor to spread from the ridge crest to the 

trenches. Therefore, the oldest fossils found on the sea floor 

are no more than 180 million years old. 

5. In 1962, President John F. Kennedy appointed Hess as 

Chairman of the Space Science Board -an advisory group for 

the National Aeronautics and Space Administration (NASA). 

During the late 1960s, Hess helped plan the first landing of 

humans on the moon. He was part of a committee assigned to 

analyze rock samples brought back from the moon by the 

Apollo 11 crew. 

6. In 1984, the American Geophysical Union established the 

Harry H. Hess medal in recognition of “outstanding 

achievements in research in the constitution and evolution of 

Earth and sister planets.” 

over stationary “hotspots” in the earth’s mantle and form 

volcanic islands. 

4. In 1965, Wilson proposed that a type of plate boundary must 

connect ocean ridges and trenches. He suggested that a plate 

boundary ends abruptly and transforms into major faults that 

slip horizontally. Wilson called these boundaries “transform 

faults”. 

5. In 1967, Wilson published an article that described the 

repeated process of ocean basins opening and closing-a 

process later named the Wilson Cycle. Geologists believe that 

the Atlantic Ocean basin closed millions of years ago and 

caused the formation of the Appalachian and Caledonian 

mountain systems. The basin later re-opened to form today’s 

Atlantic Ocean. 

6. Antarctica 

D. African Plate 

E. Indo-Australian Plate 

F. Antarctic Plate

Practice 2: 

1. First problem is done for students. 

Station A: t p = 128 seconds 

2. Station B: 

5 km/sec × t p = 3 km/sec × (t p + 80 sec) 

(2 km/sec) t p = 240 km 

t p = 120 seconds 

3. Station C: t p = 180 seconds 

4. Station A: distance = 5 km/s × 128 sec = 640 km 

Station B: distance = 5 km/s × 120 sec = 600 km 

Station C: distance = 5 km/s × 180 sec = 900 km 


(a) 5 km/s × 200 s = 3 km/s × (200 s + x) 

1000 km = 600 km + (3 km/s)x 

400 km = (3 km/s)x 

x = 133 s = time between the P-waves and S-waves 

(b) 133 s + 200 s = 333 s = t s 

Skill Sheet 20.2: Volcano Parts 

A. Vent 

B. Layers of lava and ash 

C. Volcano 

D. Magma 

Skill Sheet 20.3: Basalt and Granite 

Sample student answer: 

Skill Sheet 21.2: Concentration of Solutions 

1. 6.7% 

2. 2.0% 

3. 0.6% 

4. 400 g salt 

5. 3.75 g sugar 

6. 139 g sand 

Page 46 of 57 

6. Table 3 answers: 

Variables Station 1 Station 2 Station 3 

Speed of P-waves rp 5 km/s 5 km/s 5 km/s 

Speed of S-waves r s 3 km/s 3 km/s 3 km/s 

Time between the 

arrival of P- and 

S-waves 

Total travel time of 

P-waves 

Total travel time of 

S-waves 

E. Conduit 

F. Magma chamber 

G. Vent 

H. Lava 

7. 43% 

8. 12.5 g 

9. 0.5% 

10. 8.8 g red food coloring 

t s –t p 

t p 

t s 

70 

seconds 

105 

seconds 

175 

seconds 

115 

seconds 

173 

seconds 

288 

seconds 

92 

seconds 

138 

seconds 

230 

seconds 

Distance to epicenter d p , d s 525 km 865 km 690 km 

Scale distance to 

epicenter 

2.6 cm 4.3 cm 3.5 cm

Skill Sheet 21.2: Solubility 


1. Insoluble means that no amount of this substance will 

dissolve in water at this temperature under these conditions. 

Chalk and talc are substances that do no interact with water 

molecules. It is possible that the bonds in chalk and talc 

molecules are nonpolar. 

2. The degree to which a substance is soluble depends on the 

nature of the bonds and the size of the molecules in the 

substance. Molecules of sugar, salt, and baking soda are 

different with respect to the nature of the bonds and sizes of 

these molecules. Therefore, these molecules will each 

dissolve in water in different ways and to different degrees. 

3. 205 g 

4. 190 mL 

5. 25 mL 

6. 1 g 


2. 72 grams 

3. 10 ppt 

Substance Amount of 

substance in 

200 mL of water 

at 25°C 

Saturated, 

unsaturated, 

or supersaturated? 

Table salt (NaCl) 38 grams unsaturated 

Sugar (C12H22O11 ) 500 grams supersaturated 

Baking soda 

(NaHCO3 ) 

20 grams saturated 

Table salt (NaCl) 100 grams supersaturated 

Sugar (C12H22O11 ) 210 grams unsaturated 

Baking soda 

(NaHCO3 ) 

25 grams supersaturated 

Page 47 of 57 


1. Graphs: 

2. Gases A and B are less soluble in water as temperature 

increases. Solid A is more soluble as temperature increases. 

Solid B is slightly more soluble as temperature increases. 

3. This question may be challenging for students. Temperature 

affects gas B most dramatically. The range of solubility 

values is large, ranging from one-tenth to five-thousandths. 

4. Temperature affects the solubility of solid A more than it 

affects solid B. 

5. Solid B 

6. In fall and winter, when the weather turns cold, the water will 

have more dissolved oxygen. During the warmer months of 

the spring and summer the amount of dissolved oxygen in the 

water will decrease. 

Skill Sheet 21.2: Salinity and Concentration problems 


4. Add 420 grams of salt to 1,580 grams of water. If the 

Place 

Salton Sea 

California 

Salinity 

44 

Salt in 1 L 

44 

Pure water in 1 L 

956 

dissolved salt does not bring the volume up to 2,000 mL, 

make a second batch of solution. Add the second batch to the 

first until you have two liters of solution. 

5. 6 ppt 

Great Salt 

Lake Utah 

Mono Lake 

California 

Pacific Ocean 

280 

210 

87 

280 

210 

87 

720 

790 

913 

6. 45 grams 

7. 2 ppm 

8. 5 ppb 

9. yes; yes 

10. 50,000 times more sensitive

Skill Sheet 21.3: Calculating pH 

1. Answers: 

a. 10 –2 > 10 –3 

b. 10 –14 < 10 1 

c. 10 –7 = 0.0000001 

d. 10 0 < 10 1 

2. Answers: 

a. acid 

b. neutral 

c. base 

Skill Sheet 22.1: Groundwater and Wells 


a. 1,3 

b. 3 

c. No, because water can’t pass through the cling wrap/foam 

layer. 

Thinking about what you observed: 

a. 1,3; yes 

b. 3; yes 

c. Aquiclude 

d. Aquifer 

e. No, because the well is below the aquiclude. Yes, 

hypothesis was correct. 

Skill Sheet 22.2: The Water Cycle 


A. condensation 

B. precipitation 

C. percolation 

D. groundwater flow 

E1. evaporation 

E2. evaporation 

F. transpiration 

G. water vapor transport. 

Skill Sheet 24.1: Period and Frequency 

1. 0.05 sec 

2. 0.005 sec 

3. 0.1 Hz 

4. 3.33 Hz 

5. period = 2 sec; frequency = 0.5 Hz 

6. period = 0.25 sec; frequency = 4 Hz 

7. period = 0.5 sec; frequency = 2 Hz 

Page 48 of 57 

3. pH = 4 

4. pH 5; weaker acid 

5. pH 7; Water is neutral and has an equal number of H+ and 

OH- ions. 

6. 10 –11 ; base 

7. 1 × 10 –8.4 

8. The product with lemon juice contains a greater concentration 

of acid which would mean that it might be a better cleaning 

solution than the cleaner with the weaker acid, vinegar. 

f. The surface contamination would move toward well #1. If 

well #2 was being pumped, it would not have an effect on 

the movement of surface contamination because it is 

located below the aquiclude. 

g. Well #3 would possibly be able to provide water. It 

depends on how low the water table became. 

h. It might pull in salt water from the ocean. That is a form 

of contamination. 

i. Answers will vary. Sample answer: Look up how low the 

water table got during the worst drought of the last 100 

years. Dig the well a little lower than that level. 


1. evaporation—The Sun’s heat provides energy to enable water 

molecules to enter the atmosphere in the gas phase; 

transpiration—The Sun’s energy makes photosynthesis 

possible, which in turn causes plants to release water into the 

atmosphere in a process known as transpiration. 

2. Wind pushes water in the atmosphere to new locations, so that 

the water doesn’t always fall back to Earth as precipitation in 

the same spot from which it evaporated. 

3. Gravity causes water to run down a mountain toward the 

coast, and causes water droplets to fall to Earth as 

precipitation. Gravity is also the primary force that moves 

water from Earth’s surface through the ground to become 

groundwater. 


a. 5 sec 

b. 5 sec 

c. 0.2 Hz 


a. 120 vibrations 

b. 2 vibrations 

c. 0.5 sec 

d. 2 Hz

Skill Sheet 24.1: Harmonic Motion Graphs 


a. A = 5 degrees; B = 100 cm 

b. A = 1 second; B = 2 seconds 


a. Diagram: 

Skill Sheet 24.2: Waves 

1. Diagram: 

a. Two wavelengths 

b. The amplitude of a wave is the distance that the wave 

moves beyond the average point of its motion. In the 

graphic, the amplitude of the wave is 5 centimeters. 


a. Diagram: 

Skill Sheet 24.2: Wave Interference 

1. Diagram: 

2. 4 blocks 

3. 2 blocks 

4. 32 blocks 

5. 4 blocks 

6. 1 wavelength 

7. 8 wavelengths 

Page 49 of 57 

b. Diagram: 

b. Diagram: 

3. 10 m/s 

4. 5 m 

5. 10 Hz 

6. frequency = 0.5 Hz; speed = 2 m/s 

7. frequency = 165 Hz; period = 0.006 s 

8. A’s speed is 75 m/s, and B’s speed is 65 m/s, so A is faster. 


a. 4 s 

b. 0.25 Hz 

c. 0.75 m/s 

8. A portion of the table and a graphic of the new wave are 

shown below. The values for the third column of the table are 

found by added the heights for wave 1 and wave 2. 

x 

(blocks) 

Height wave 1 

(blocks) 

Height wave 2 

(blocks) 


+2 (blocks) 

0 0 0 0 

1 0.8 2 2.8 

2 1.5 0 1.5 

3 2.2 –2 0.2 

4 2.8 0 2.8 

5 3.3 2 5.3 

6 3.7 0 3.7 

7 3.9 –2 –1.9 

8 4 0 4

Question 8 (con’t) 9. The new wave looks like the second wave, but it vibrates 

about the position of the first wave, rather than about the zero 

line. 

Skill Sheet 24.3: Decibel Scale 

1. Twice as loud. 

2. 55 dB 


a. 80 dB 

b. 60 dB 

4. Four times louder 

Skill Sheet 24.3: Human Ear 

a. Ear canal—leads to the middle ear. 

b. Eardrum—vibrates as the sound waves reach it. 

c. Semicircular canals—balance. 

d. Cochlea—a spiral-shaped, fluid-filled cavity that contains 

nerve endings and is essential to interpreting sound waves. 

Skill Sheet 24.3: Waves and Energy 

1. Most of the stone’s kinetic energy is converted into water 

waves and the waves carry that energy away from where the 

stone landed. 

2. The frequency of the jump rope increases and the energy 

expended by Ian and Igor increases for this demonstration. 

3. The 100-hertz wave has more energy. 

4. During a hurricane, waves have more energy as indicated by 

their higher amplitude. 

5. A wave that has a 3-meter amplitude has more energy than a 

wave that has a 0.03 meter (3 centimeter) amplitude. 

Skill Sheet 24.3: Standing Waves 


a. A = 2nd; B = 3rd; C = 1st or fundamental; D = 4th (You 

can easily determine the harmonics of a vibrating string 

by counting the number of “bumps” on the string. The 

first harmonic (the fundamental) has one bump. The 

second harmonic has two bumps and so on.) 

b. Diagram: 

Page 50 of 57 


a. 30 dB 

b. 50 dB 

c. 70 dB 

e. Malleus—transfers vibrations from the eardrum. 

f. Incus—between the malleus and stapes; transmits vibrations 

from malleus to stapes. 

g. Stapes—vibrates against the cochlea. 

6. The low-volume sound has the least amount of energy. 

7. Visible light waves are likely to have greater energy. 

8. This wave has more energy and a higher frequency than the 

other waves. Sketch: 

c. A = 1 wavelength, B = 1.5 wavelengths, C = half a 

wavelength, D = 2 wavelengths 

d. A = 3 meters, B = 10 meters, C = 6 meters, D = 7.5 meters 


a. Diagram: 

b. See answer for (c).

c. See table below: 

Harmonic Speed (m/sec) Wavelength 

(m) 

Frequency (Hz) 

1 36 24 1.5 

2 36 12 3 

3 36 8 4.5 

4 36 6 6 

5 36 4.8 7.5 

6 36 4 9 

d. The frequency decreases as the wavelength increases. 

They are inversely proportional. 

Skill Sheet 25.1: The Electromagnetic Spectrum 

1. Green 

2. Green 

3. 400 × 10 –9 m or 4.0 × 10 –7 m 

4. 517 × 10 12 Hz or 5.17 × 10 14 Hz 

5. 652 × 10 –9 m or 6.52 × 10 –7 m 

6. 566 × 10 12 Hz or 5.66 × 10 14 Hz 

λ 

1 

f 

2 

7. The answer is: ----- = ---- 

λ 2 

f 1 

8. λ = 0.122 meter or 1.22 × 10 –1 m 

9. λ = 3.3 meters 

Skill Sheet 25.2: Color Mixing 

1. The differences include: (1) for RGB the primary colors are 

red, green, and blue and for CMYK the primary colors are 

cyan, magenta, and yellow, (2) for RGB black is the absence 

of light but for CMYK black is an added pigment, and (3) to 

make white with RGB you mix the three primary colors and 

to make white in CMYK you omit pigment (or you need a 

special white pigment to make white, as in making white 

paint). 

2. (a) Your eye sees red. (b) Your eye sees magenta. (c) Your eye 

sees green. (d) Your eye sees cyan. 

3. The blue and red photoreceptors would be stimulated to see 

purple. For purple, the signal for blue would be stronger. 

Note: This can be tested for purple or any color by adjusting 

the RGB intensity for font color in a word processing 

program. 

4. To see yellow, the red and green photoreceptors of your eyes 

are stimulated. 

5. By reflecting most of the light that strikes it, all the colors of 

visible light reach your eyes and all three photoreceptors (red, 

green, and blue) are stimulated so that your brain interpret the 

color as being white. 

6. (a) All three colors of light would be mixed, (b) There would 

be an absence of light, (c) green and blue light would be 

mixed in equal amounts, (d) red and green light would be 

mixed in equal amounts. 

7. (a) red light is reflected and all the other colors are absorbed, 

(b) red light is reflected and no colors of light are absorbed (c) 

blue light is absorbed and no light is reflected so that the 

apple appears black. 

Page 51 of 57 

e. See table below. 

Harmonic Speed (m/sec) Wavelength 

(m) 

Frequency (Hz) 

1 36 12 3 

2 36 6 6 

3 36 4 9 

4 36 3 12 

5 36 2.4 15 

6 36 2 18 

f. The shorter rope resulted in harmonics with shorter 

wavelengths. The second harmonic on the short rope is 

equivalent in terms of wavelength and frequency to the 

4th harmonic on the longer rope. 

10. f = 6 × 10 16 Hz 

11. 1.0 × 10 15 Hz 

12. 1.0 × 10 –4 m 


a. f = 3 × 10 19 hertz 

b. It is the minimum frequency. 

14. radio waves, microwaves, infrared, visible, ultraviolet, 

X rays, and gamma rays 

15. gamma rays, X rays, ultraviolet, visible, infrared, 

microwaves, and radio waves 

8. Table answers: 

CMYK color model 

Mixed colors Reflected color Which colors of light are absorbed? 

magenta + red green absorbed by magenta 

yellow 

blue absorbed by yellow 

yellow + green blue absorbed by yellow 

cyan 

red absorbed by cyan 

cyan + 

magenta 

blue red absorbed by cyan 

green absorbed by magenta 

9. If magenta and cyan paint are mixed, you get blue paint. 

10. (a) The color green is made by mixing yellow and cyan. 

(b) The green photoreceptors in your eyes are stimulated by 

this color combination and the brain interprets the color as 

green. 

(c) Sample diagram:

Skill Sheet 25.2: The Human Eye 

a. Cornea—refracts and focuses light. 

b. Iris—pigmented part of the eye that opens or closes to change 

the size of the pupil. 

c. Ciliary muscles—contract to change the shape of the lens. 

d. Sclera—outer protective covering. 

e. Vitreous humor—liquid inside of the eye. 

f. Optic nerve—transmits signals from the retina to the brain. 

Skill Sheet 25.3: Measuring Angles 

Answers are: 

Letter Angle Letter Angle 

A 56° J 153° 

Skill Sheet 25.3: Using Ray Diagrams 

1. A is the correct answer. Light travels in straight lines and 

reflects off objects in all directions. This is why you can see 

something from different angles. 

2. C is the correct answer. In this diagram, when light goes from 

air to glass it bends about 13 degrees from the path of the light 

ray in air. The light bends toward the normal to the air-glass 

surface because air has a lower index of refraction compared 

to glass. When the light re-enters the air, it bends about 

13 degrees away for the light path in the glass and away from 

the normal. 

As a ray of light approaches glass at an angle, it bends 

(refracts) toward the normal. As it leaves the glass, it bends 

away from the normal. However, if a ray of light enters a 

piece of glass perpendicular to the glass surface, the light ray 

will slow, but not bend because it is already in line with the 

normal. This happens because the index of refraction for air is 

lower than the index of refraction for glass. The index of 

refraction is a ratio that tells you how much light is slowed 

when it passes through a certain material. 

Skill Sheet 25.3: Reflection 

1. Diagram at right: 

2. The angle of reflection will 

be 20 degrees. 

3. Each angle will measure 45 

degrees. 

B 110° K 131° 

C 10° L 148° 

D 96° M 81° 

E 167° N 90° 

F 122° O 73° 

G 34° P 27° 

H 45° Q 139° 

I 19° 

Page 52 of 57 

g. Retina—thin layer of cells in the back of the eye that converts 

light into nerve signals. 

h. Choroid—provides oxygen and nutrients to the retina. 

i. Lens—refracts and focuses light. 

j. Aqueous humor—liquid in the front part of the eye. 

k. Pupil—opening in the iris that controls the amount of light 

entering the eye. 

3. A is the correct answer. Light rays that approach the lens that 

are in line with a normal to the surface pass right through, 

slowing but not bending. This is what happens at the principal 

axis. However, due to the curvature of the lens, the parallel 

light rays above and below the principal axis, hit the lens 

surface at an angle. These rays bend toward the normal (this 

bending occurs toward the fat part of the lens) and are focused 

at the lens’ focal point. The rays diverge (move apart) past the 

focal point. 

4. Diagram: 

4. Diagram at right: 

5. The angle is 72 degrees. 

Therefore, the angles of 

incidence and reflection 

will each be 36 degrees. 

6. The angles of 

incidence and 

reflection at point A 

are each 70 degrees; 

the angles of incidence 

and reflection at point 

B are each 21 degrees.

Skill Sheet 25.3: Refraction 


1. The index of refraction will never be less than one because 

that would require the speed of light in a material to be faster 

than the speed of light in a vacuum. Nothing in the universe 

travels faster than that. 

2. The index of refraction for air is less than that of glass 

because a gas like air is so much less dense than a solid like 

glass. The light rays are slowed each time they bump into an 

atom or molecule because they are absorbed and re-emitted 

by the particle. A light ray in a solid bumps into many more 

particles than a light ray traveling through a gas. 

3. water: 2.26 × 10 8 ; glass: 2.0 × 10 8 ; diamond; 1.24 × 10 8 

4. speed up 

Skill Sheet 25.3: Drawing Ray Diagrams 

1. Diagram: 

The image 

is inverted 

as 

compared 

with the 

object. 

Skill Sheet 26.1: Astronomical Units 

1. 9.53 AU 

2. 0.72 AU 

3. 58 million kilometers 

4. 2.87 billion kilometers 

5. Less. The moon is not nearly as far from Earth as the Sun. 

Page 53 of 57 

5. slow down 


1. The light ray is moving from low-n to high-n so it will bend 

toward the normal. 

2. The light ray is moving from high-n to low-n so it will bend 

away from the normal. 

3. The difference in n from diamond to water is 1.09 while the 

difference from sapphire to air is 0.770. The ray traveling 

from diamond to water experiences the greater change in n so 

it would bend more. 

4. From left to right, material B is water, emerald, helium, cubic 

zirconia. 

2. Diagram: 

3. A lens acts like 

a magnifying 

glass if an 

object is placed 

to the left of a 

converging lens 

at a distance 

less than the 

focal length. 

The lens bends the rays so that they appear to be coming from 

a larger, more distant object than the real object. These rays 

you see form a virtual image. The image is virtual because the 

rays appear to come from an image, but don’t actually meet. 

6. Uranus 

7. Mercury 

8. Saturn 

9. Saturn 

10. yes 

Skill Sheet 26.1: Gravity Problems 

Table 1 answers: 1. 9.5 pounds on Neptune 

Planet Force of gravity in Value compared to 2. 1,029 newtons on Saturn 

Newtons (N) 

Earth’s gravity 3. The baby weighs 44.1 Newtons on Earth which is equal to 9.8 

Mercury 

Venus 

Earth 

3.7 

8.9 

9.8 

0.38 

0.91 

1 

pounds. 

4. Venus, Jupiter, Neptune, Pluto, then Saturn 

5. Answer: 

Mars 

Jupiter 

Saturn 

3.7 

23.1 

9.0 

0.38 

2.36 

0.92 

−11 

2 24 26 

⎛6.67× 10 Nm i 

⎞(6.4× 

10 )(5.7× 10 ) 

Gravity = ⎜ 2 ⎟ 

11 2 

⎝ kg ⎠ (6.52× 10 ) 

Uranus 8.7 0.89 

17 

= 5.72× 10 N 

Neptune 11.0 1.12 

Pluto 0.6 0.06 

Skill Sheet 26.1: Universal Gravitation 

1. F =9.34× 10 –6 N. This is basically the force between you 

and your car when you are at the door. 

2. 5.28 × 10 -10 N 

3. 4.42 N 

4. 7.33 × 10 22 kilograms 


a. 9.8 N/kg = 9.8 kg-m/sec 2 -kg = 9.8 m/sec 2 

b. Acceleration due to the force of gravity of Earth. 

c. Earth’s mass and radius. 

6. 1.99 ×10 20 N 

7. 4,848 N 

8. 3.52 × 10 22 N

Skill Sheet 26.1: Nicolaus Copernicus 

1. Because he was from a privileged family, young Copernicus 

had the luxury of learning about art, literature, and science. 

When Copernicus was only 10 years old, his father died. 

Copernicus went to live his uncle who was generous with his 

money and provided Copernicus with an education from the 

best universities. Copernicus lived during the height of the 

Renaissance period when men from a higher social class were 

expected to receive well-rounded educations. 

2. Copernicus’ uncle, Lucas Watzenrode, was a prominent 

Catholic Church official who became bishop of Varmia in 

1489. After Copernicus finished four years of study at the 

University of Krakow, Watzenrode appointed Copernicus a 

church administrator. Copernicus used his church wages to 

help pay for additional education. While studying at the 

University of Bologna, Copernicus’ passion for astronomy 

grew under the influence of his mathematics professor, 

Domenico Maria de Novara. Copernicus lived in his 

professor’s home where they spent hours discussing 

astronomy. 

3. Copernicus examined the sky from a tower in his uncle’s 

palace. He made his observations without any equipment. 

4. Prior to the 1500s, most astronomers believed that Earth was 

motionless and the center of the universe. They also thought 

that all celestial bodies moved around Earth in complicated 

patterns. The Greek astronomer Ptolomy proposed this 

geocentric theory more than 1000 years earlier. 

Skill Sheet 26.1: Galileo Galilei 

1. “On Motion” described how a pendulum’s long and short 

swings take the same amount of time. 

2. Galileo’s many inventions include the thermometer, water 

pump, military compass, microscope, telescope, and 

pendulum clock. Information and illustrations of the 

inventions can be found using the Internet or library. 

3. Galileo observed the motion of Jupiter’s moons and realized 

that despite what Ptolemy said, heavenly bodies do not 

revolve exclusively around Earth. He also realized that his 

observation of the phases of Venus showed that Venus was 

revolving around the sun, not around Earth. Galileo therefore 

Skill Sheet 26.1: Johannes Kepler 

1. Copernicus’ idea that the sun was at the center of the solar 

system was revolutionary because people believed Earth was 

the center of the universe. 

2. Brahe helped Kepler make his important discoveries in 

several ways. Brahe invited Kepler to come and work with 

him. He asked Kepler to solve the problem of Mars’ orbit. 

When Brahe died, Kepler gained all of his observational 

records. Kepler also got Brahe’s job. 

3. Kepler used mathematics to solve problems in astronomy. For 

this reason, Kepler is considered a theoretical positional 

astronomer. Brahe was an observational astronomer. He made 

and recorded the motion of planets and the stars in the night 

sky without a telescope. Galileo was also an observational 

astronomer. He used and improved the telescope, but he was 

not a mathematician. 

4. Kepler’s discovery that Mars traveled in an elliptical orbit 

was different than Copernicus’ theory which said planets 

traveled in circular orbits. 

5. Kepler’s three laws of planetary motion are: 

Planets orbit the sun in an elliptical orbit with the sun in 

one of the foci. 

Page 54 of 57 

5. Copernicus believed that the universe was heliocentric (suncentered), 

with all of the planets revolving around the sun. He 

explained that Earth rotates daily on its axis and revolves 

yearly around the sun. He also suggested that Earth wobbles 

like a top as it rotates. Copernicus’ theory led to a new 

ordering of the planets. In addition, it explained why the 

planets farther from the sun sometimes appear to move 

backward (retrograde motion), while the planets closest to the 

sun always seem to move in one direction. This retrograde 

motion is due to Earth moving faster around the sun than the 

planets farther away. 

6. At the time, Church law held great influence over science and 

dictated a geocentric universe. 

7. The Copernicus Satellite, or Orbiting Astronomical 

Observatory 3 (OAO-3) was a collaborative project of both 

the United States’ National Aeronautics and Space 

Administration (NASA) and the United Kingdom’s Science 

and Engineering Research Council (SERC). The satellite 

operated from August 1972 to February 1981. The main 

experiment on the satellite was a Princeton University 

ultraviolet (UV) telescope. An x-ray astronomy experiment 

created by the University College London/Mullard Space 

Science Laboratory was also onboard. The Copernicus 

Satellite gathered a series of high-resolution ultraviolet 

spectral scans of over 500 objects, most of them being bright 

stars. 

concluded that Copernicus’ assertion that the sun, not Earth, 

was at the center must be correct. 

4. Answers will vary. Students might suggest that Galileo use a 

less abrasive approach to convince people that the Copernican 

view is correct. 

5. Galileo’s telescope is the most likely student response, 

because it so profoundly changed our understanding of the 

solar system. However, students may choose another 

invention as long as they provide valid reasons for their 

decision. 

The law of areas says that planets speed up as they travel 

in their orbit closer to the sun and they slow down as they 

travel in their orbit farther away from the sun. 

The harmonic law says that a planet’s distance from the 

sun is mathematically related to the amount of time it 

takes the planet to revolve around the sun. 

6. Three examples of a paradigm shift: 

Copernicus’ theory that the sun and not Earth was the 

center of the solar system. 

Kepler’s discovery that planets orbit the sun in an 

elliptical and not a circular path. 

Newton’s laws of gravitational attraction.

Skill Sheet 26.1: Measuring the Moon’s Diameter 


There are no questions to answer for Part 1. 


1. AC = 6 cm 

AD = 6 cm 

AB = 2 cm 

AE = 2 cm 

BE = 2 cm 

CD = 6 cm 

2. Distance AB is 1/3 of the distance AC 

3. Distance BE is 1/3 of the distance CD 

4. If a triangle is drawn inside a larger triangle so that they share 

the same vertex and have bases that are parallel, then the sides 

Skill Sheet 26.2: Benjamin Banneker 

1. An understanding of gear ratios was necessary for building 

the clock. He used geometry skills to figure out how to create 

a large-scale model of each tiny piece of the watch he 

examined. 

2. Personal strengths identified from the reading include strong 

spacial skills (building the clock), creativity and problem 

solving skills (irrigation system), curiosity and attention to 

detail (astronomical observations, cicada observations, and 

almanac), concern for others (letter to Jefferson). 

3. Dates are as follows: 

a. 1863 

b. 1865 

c. 1920 

d. 1954 

4. Any three of the following answers is correct. Banneker’s 

accomplishments include: 

a. Designed an irrigation system 

b. Documented cycle of 17-year cicada 

c. Published detailed astronomical calculations in popular 

almanacs 

Skill Sheet 26.3: Touring the Solar System 


Legs of the trip Distance Hours Days Years 

travelled for 

each leg (km) 

travelled travelled travelled 

Earth to Mars 78,000,000 86,666 3,611 9.9 

Mars to Saturn 1,202,000,000 1,335,600 55,648 152 

Saturn to Neptune 3,070,000,000 3,411,100 142,130 389 

Neptune to Venus 4,392,000,000 4,880,000 203,330 557 

Venus to Earth 42,000,000 46,667 1,944 5.3 


1. 

2. 

8 glasses 3,611 days = 28,888 glasses of water 

1 day × 

2, 000 food calories 

× 

203, 330 days = 

1 day 

406,660,000 food calories 

Skill Sheet 27.1: The Sun: A Cross-Section 

A. Corona 

B. Chromosphere 

C. Photosphere 

Page 55 of 57 

and base of the small triangle will be proportional to the sides 

and base of the large triangle. 


Answers will vary. A string distance of about 1 meter will 

yield good results. 


1. A and D are the same, but D is most helpful because it is set 

up with the unknown in the numerator. 

2. Answers will vary. A string distance of about 1 meter should 

give a value close to the accepted moon diameter; 3,476,000 

meters. 

3. The semi-circle diameter is the base of the small triangle; the 

base of the large triangle is what we are solving for: the 

d. Served as surveyor of territory that became Washington 

D.C. 

5. Banneker evidently had a strong innate curiosity about the 

natural world. He was passionate about improving the welfare 

of the black men and women in the United States and his 

letter to Jefferson stated that he hoped his scientific work 

would be seen as proof that people of all races are created 

equal. 

6. Banneker’s puzzles can be found on several web sites. Using 

an Internet search engine, look for “Benjamin Banneker” + 

puzzle. Some of the sites publish the answers while others do 

not. Here is one of Banneker’s puzzles taken from the web 

site www.thefriendsofbanneker.org. Note that the puzzle was 

written in the 1700’s and is from Banneker’s personal 

journals. 

THE PUZZLE ABOUT TRIANGLES 

“Suppose ladder 60 feet long be placed in a Street so as to 

reach a window on the one side 37 feet high, and without 

moving it at bottom, will reach another window on the other 

side of the Street which is 23 feet high, requiring the breadth 

of the Street.” [No solution recorded in historic records.] 

3. Pack foods high in fat for the journey because you get more 

calories per gram than from proteins and carbohydrates and 

you want a payload minimum. 

4. Your entire trip will take 1,113 years, so you will need that 

many turkeys. 


1. Jupiter; it has 39 moons. 

2. Venus has the hottest surface temperature; Neptune has the 

coldest surface temperature. 

3. Venus; it takes 243 Earth days to rotate once around its axis. 

4. Jupiter has the shorter day; it takes 0.41 Earth days to rotate. 

5. Jupiter; it has the strongest gravitational force. You will 

weigh 2.36 times your Earth weight in Newtons. 

6. Jupiter; it has the largest diameter of 142,796 km. 

7. Jupiter; it has the strongest gravitational force, therefore the 

spaceship must orbit at a fast speed to balance the 

gravitational force pulling the spaceship towards Jupiter’s 

surface. 

D. Convection zone 

E. Radiation zone 

F. Core

Skill Sheet 27.1: Arthur Walker 

1. You may wish to have students compare and contrast their 

definitions with those of a student who used a different 

source. Discuss with the class the value of using a variety of 

sources and the importance of crediting these sources. 

2. Walker didn’t allow prejudice to dissuade him from pursuit of 

his goals. As a result he made important contributions to 

science and society. He also spent time and energy helping 

other members of minority groups achieve their own goals. 

3. A spectrometer separates light into spectral lines. Each 

element has its own unique pattern of lines, so scientists use 

the patterns to identify the ions in the corona. Temperature 

can be determined by the colors seen in the corona. For 

example, red indicates cooler areas, while bluish light 

indicates a very hot area. 

4. Magazines and journals that may have one of Walker’s 

photographs can be found at public and university libraries. 

You might suggest that students contact a reference librarian 

for assistance. 

5. The committee found that the accident was caused by a 

failure in a seal of the right solid rocket booster. They also 

made nine specific recommendations of changes to be made 

Skill Sheet 27.2: The Inverse Square Law 

1. 0.25 W/m 2 

2. one-ninth 

3. 24,204 km (four times the original distance) 

Skill Sheet 28.1: Scientific Notation 


a. 122,200 

b. 90,100,000 

c. 3,600 

d. 700.3 

e. 52,722 

Skill Sheet 28.1: Understanding Light Years 

1. 5.7 × 1013 km 

2. 4.3 × 1019 km 

3. 3.8 × 10 10 km 

4. 5,344 ly 

5. 1.16 × 10 –12 ly 

6. 1.16 ly 

Skill Sheet 28.1: Parsecs 

1. 1.84 pc 

2. 1.38 × 106 pc 

3. 1.23 × 10-3 pc 

4. 2.55 × 101 pc or 25.5 pc 

5. 4.85 × 10-4 pc 

Skill Sheet 28.1: Edwin Hubble 


spectroscopy—a method of studying an object by 

examining the visible light and other electromagnetic 

waves it creates. 

cosmology—the astrophysical study of the history, 

structure, and constituent dynamics of the universe. 

Page 56 of 57 

to the space shuttle program prior to another flight. These 

steps included: 

a. Redesign the solid rocket boosters. 

b. Upgrade the space shuttle landing system. 

c. Create a crew escape system that would allow astronauts 

to parachute to safety in certain situations. 

d. Improve quality control in both NASA and contractor 

manufacturing. 

e. Reorganize the space shuttle program to place astronauts 

in key decision-making roles. 

f. Revoke any waivers to current safety standards, especially 

those related to launches in poor weather conditions. 

g. Open the review of a mission’s technical issues to 

independent government agencies. 

h. Set up an extensive open review system to evaluate issues 

related to each particular mission. 

i. Provide a means of anonymous, reprisal-free reporting of 

space shuttle safety concerns by any NASA employee or 

contractor. 

4. 55.6 N 

5. It is 9 times more intense 2 meters away. 

6. It is 16 times more intense at 1 meter than at 4 meters away. 


a. 4.051 × 10 6 

b. 1.3 × 10 9 

c. 1.003 × 10 6 

d. 1.602 × 10 4 

e. 9.9999 × 10 12 

7. 1,200 ly 

8. 8.0478 × 10 14 km 

9. 4,280,056,000 km, or 4.28 × 10 9 km 

10. 0.000026336 AU, or 2.6 × 10 –5 AU 

11. 63,288 AU 

6. 54.8 pc 

7. 30,000 pc 

8. 770,000 pc 

9. 26 pc 

10. 1.44 × 10 -4 pc 

2. Outstanding students from around the world are nominated for 

the prestigious Rhodes scholarship. Rhodes Scholars are invited 

to study at the University of Oxford in England. Only about 90 

students are selected each year. This scholarship is awarded by 

the Rhodes Trust, a foundation set up by Cecil Rhodes in 1902. 

3. A larger telescope allows more light to be collected by the 

mirrors and/or lenses of the telescope. More light allows for a 

clearer image, which can then be magnified to show greater 

detail.

4. Example answer: Edwin was incredibly excited today. Albert 

Einstein came to visit him, and he even thanked him for all of 

his hard work. It’s almost unbelievable! The most celebrated 

scientist of our lifetime came to visit him. Just to be associated 

with Einstein is an honor, let alone be thanked by him. Edwin 

works very hard, and he must be very proud of his new 

discoveries that have changed the world of astronomy. 

Skill Sheet 28.2: Light Intensity 

1. Example problem: 4.8 W/m 2 

2. 0.0478 W/m 2 

3. 0.0119 W/m 2 

4. If distance from a light source doubles, then light intensity 

decreases by a factor of 4. Example: 4 × 0.0119 W/m 2 

approximately equals 0.0478 W/m 2 (see questions 2 and 3). 


Skill Sheet 28.2: Henrietta Leavitt 

1. Leavitt discovered new variable stars by comparing 

photographic plates. The photographs showed the same 

regions in the sky, but at different times. This allowed Leavitt 

to examine the photos and identify stars that had changed in 

size over time. 

2. Leavitt studied Cepheid stars and found an inverse relationship 

between a star’s brightness cycle and its magnitude. A stronger 

star took longer to cycle between brightness and dimness. As a 

result, she developed the Period-Luminosity relation. 

3. The asteroid is called 5383 Leavitt. 

4. The observatory was founded in 1839 and currently conducts 

research in astronomy and astrophysics. 

5. Example Answers: 

Ejnar Hertzsprung: 

Danish astronomer born October 8, 1873 

Found the distance to the Small Magellan Cloud located 

outside of the Milky Way Galaxy in 1913. 

Skill Sheet 28.2: Calculating Luminosity 

1. luminosity = 30 watts 

power rating on bulb = 300 watts 

2. luminosity = 1 watt 

power rating on bulb = 10 watts 

Skill Sheet 28.3: Doppler Shift 


1. Graphic, right 

2a. B and D 

2b. A and C 

2c. C 

2d. B 

Page 57 of 57 

5. The fact that the universe is expanding implies that it must 

have been smaller in the past than it is today. The expanding 

universe implies that the universe must have had a beginning. 

This idea led to the development of the Big Bang theory, 

which says that the universe exploded outward from a single 

point smaller than an atom into the vast expanse of today’s 

universe. 

a. 0.005 W/m 2 

b. 0.05 W/m 2 

c. 0.5 W/m 2 

d. 5 W/m 2 

6. The watts of a light source and light intensity are directly 

related. This means that if you use a light source that has 10 

times the wattage, then light intensity will increase 10 times. 

Developed the Hertzsprung-Russell diagram which 

graphs the magnitude of stars against their surface 

temperature or color. 

Harlow Shapley: 

Astronomer born November 2, 1885 in Nashville, 

Missouri 

In addition to being an astronomer, Shapley was a writer. 

Shapley determined the size of the Milky Way Galaxy. 

Edwin Hubble: 

Astronomer born November 29, 1889 in Marshfield, 

Missouri. 

Earned an undergraduate degree in math and astronomy, 

and went on to study law. 

Developed a classification system for galaxies and created 

Hubble’s Law which helped astronomers determine the 

age of the universe. 

3. Challenge: 

luminosity = 1.370 × 10 3 (4π)(1.5 × 10 11 ) 2 

= 1.370 × 10 3 (4π)(2.25 × 10 22 ) 

= 39 × 10 25 

= 3.9 × 10 26 watts 


1. The star is moving away from Earth at a speed of 

5.6 × 10 6 m/s. 

2. The star is moving toward Earth at a speed of 

8.6 × 10 6 m/s. 

3. Galaxy B is moving fastest because it has shifted farther 

toward the red (15 nm) than Galaxy A (9 nm). 

4. It supports the Big Bang. This theory states that the universe 

began from a single point and has been expanding ever since.

PES Skill Sheets.book - Capital High School

Create successful ePaper yourself

Delete template?

Save as template?