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Derived laws and system of forces
- 1. Shaik Nayeem Engineering Mechanics Introduction: Derived Laws and System of forces 1 Shaik Nayeem
- 2. • Derived Laws • Triangle Law of Forces • Polygon law of forces • Units in Mechanics • System of Forces • Idealisations in Mechanics Contents
- 3. Derived Laws Shaik Nayeem 3 Derived Laws Triangle law of forces Polygon law of forces
- 4. Triangle Law of Forces Shaik Nayeem 4 It is derived from the parallelogram law of forces Triangle law of forces is states that “if two forces are acting on a body are represented one after another by the sides of the triangle , their resultant is represented by the closing side of triangle taken from first point to the last point”
- 5. Polygon law of forces Shaik Nayeem 5 States that “if number of concurrent forces acting simultaneously on a body are represented in magnitude and direction by the sides of the polygon, taken in order, then the resultant is represented in magnitude and direction by the closing side of the polygon , taken from first point to last point”
- 6. Polygon law of forces(Cont…) Shaik Nayeem 6
- 7. Units in Mechanics Shaik Nayeem 7 Fundamental Units Length(L) Mass(M) Time(S) Derived Units: Sometimes, the units are also expressed in other units( which are derived from fundamental units) known as derived units ex: units of area, velocity, acceleration, pressure etc
- 8. Units in Mechanics (Cont…) Shaik Nayeem 8 SystemofUnits Meter-Kilogramme-Second (MKS) System Centimetre- Gramme –Second (CGS) System Foot- Pound- Second (FPS) System
- 9. Units in Mechanics (Cont…) Shaik Nayeem 9 Some quantities are expressed in MKS units as:
- 10. Units in Mechanics(Cont…) Shaik Nayeem 10 Another type of system of unit is SI( International System) units SI:- Meter-Kilogramme – Second The difference between MKS and SI is mainly in selecting the unit of force
- 11. Units in Mechanics(Cont…) Shaik Nayeem 11 Force ∝ 𝑀𝑎𝑠𝑠 𝑋 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 Force = k X Mass X Acceleration In SI units: a=1 m /𝒔𝒆𝒄 𝟐 Force units are: kg-m/𝑠𝑒𝑐2 is called “Newton” In MKS units: a=g = 9.81 m /𝒔𝒆𝒄 𝟐 Force in MKS units: kg-wt is called kilogramme weight 1kg-wt = 9.81 Newton
- 12. Units in Mechanics Shaik Nayeem 12 Prefixes and Symbols of multiplying factors in SI:
- 13. System of Forces Shaik Nayeem 13 SystemofForces Collinear Forces Coplanar Parallel Forces Coplanar like parallel Forces Coplanar concurrent Forces Coplanar non- concurrent Forces Non-coplanar parallel forces Non-coplanar concurrent forces Non-coplanar non-concurrent forces
- 14. Collinear Forces Shaik Nayeem 14 Collinear forces are forces which have a common line of action, i.e. the line of action of the forces lie along a single straight line.
- 15. Coplanar Parallel Forces Shaik Nayeem 15 All forces are parallel to each other and lie in single plane
- 16. Coplanar like parallel Forces Shaik Nayeem 16 All forces are parallel to each other, lie in single plane and are acting in the same direction
- 17. Coplanar concurrent Forces Shaik Nayeem 17 Line of action of all forces pass through a single point and forces lie in the same plane F1 F3 F2
- 18. Coplanar non- concurrent Forces Shaik Nayeem 18 All forces do not meet at a point, but lie in a single plane
- 19. Non-coplanar parallel forces Shaik Nayeem 19 All the forces are parallel to each other, but not in same plane
- 20. Non-coplanar concurrent forces Shaik Nayeem 20 All forces do not lie in the same plane, but their lines of action pass through a single point
- 21. Non-coplanar non-concurrent forces Shaik Nayeem 21 All forces do not lie in the same plane and their lines of action do not pass through a single point
- 22. Idealisations in Mechanics Shaik Nayeem 22 Assumptions in Mechanics The body is rigid The body can be treated as continuum It may be treated as a particleApplied force can be treated as point force Support conditions are idealized
- 23. Shaik Nayeem 23 Thank You Shaik Nayeem