2. 1© Manhattan Press (H.K.) Ltd. Work Energy Energy 3.6 Work, energy and power Power Power

3. 2 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 125) Work is done when you lift a load More work is done - lift heavier load - lift load higher work involves: - force - movement caused by force Go to More to Know 3 More to Know 3

4. 3 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 125) W = Fs cos 

5. 4 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 125) 1. F and s in same direction (  = 0) W = Fs

6. 5 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 126) 2. F and s in perpendicular (  = 90 o ) W = 0 Unit – joule (J) 1 J = 1 N m scalar Go to More to Know 4 More to Know 4

7. 6 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 126) Work done by a variable force = Area under force-displacement graph

8. 7 © Manhattan Press (H.K.) Ltd. Work 3.6 Work, energy and power (SB p. 126) e.g. = Area of triangle under the graph = W =

9. 8 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 127) Energy - ability to do work Mechanical energy - energy due to motion, position, physical condition - kinetic energy or potential energy

10. 9 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 127) Kinetic energy The kinetic energy (K or KE) is the energy of a body due to its motion. W = Fs F = ma v 2 = u 2 + 2as W = mv 2 /2 Work done by F is changed to KE of body

11. 10 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 128) Kinetic energy Kinetic energy of the body (K) = mv 2 /2 W = Fs = (ma)s = mv 2 /2 – mu 2 /2 = Increase in kinetic energy

12. 11 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 128) Potential energy An object stores energy due to its physical condition or of its position. The energy stored in the object is called potential energy (U or PE). E.g. - stretched spring or rubber band - lifting object against earth’s gravity

13. 12 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 128) Potential energy Gain in gravitational potential energy = Work done against gravitational force = Fh Potential energy (U) = mgh

14. 13 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 128) Potential energy Energy stored in stretched spring = kx 2 /2 k – force constant of spring, x - extension Obey Hooke’s Law Elastic potential energy

15. 14 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 129) Principle of Conservation of Energy Kinetic energy (K) + Potential energy (U) = Total energy (E)  K = -  U constant

16. 15 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 129) Principle of Conservation of Energy E.g. K = mv 2 /2  K = mv 2 /2 - 0 and v 2 = u 2 +2as  K = mgh = Loss in gravitational potential energy

17. 16 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 129) Principle of Conservation of Energy E.g. Gravitational force acting on man (F) = mg Work done by F (W) = Fh = mgh =  K Work done by gravitational force is converted into gain in kinetic energy

18. 17 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 130) Relationship between force and potential energy E = K + U  K = -  U W = F(  s) = -  U Force (F) =

19. 18 © Manhattan Press (H.K.) Ltd. Energy 3.6 Work, energy and power (SB p. 130) Relationship between force and potential energy E.g. U = mgs F is –ve (it is in –ve direction) Go to Example 6 Example 6 Go to Example 7 Example 7

20. 19 © Manhattan Press (H.K.) Ltd. Power 3.6 Work, energy and power (SB p. 133) Power - rate at which work is done - rate at which energy is delivered Average power =

21. 20 © Manhattan Press (H.K.) Ltd. Power 3.6 Work, energy and power (SB p. 133) F and s in same direction Power Power = Fv F and s at  Power = Fv cos  Unit – watt (W) Go to Example 8 Example 8 Go to Example 9 Example 9

22. 21 © Manhattan Press (H.K.) Ltd. Power 3.6 Work, energy and power (SB p. 135) Efficiency - percentage of useful work done compared to the input energy Efficiency < 100%

23. 22 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.1 Newton’s Laws of Motion 1. Newton’s First Law of Motion states that an object will remain at rest or move along a straight line with constant speed, unless it is acted upon by a force. 2. Momentum = Mass ×Velocity 3. Newton’s Second Law of Motion states that the rate of change of momentum of an object is directly proportional to the net force acted on it, and the motion occurs along the direction of the force.

24. 23 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.1 Newton’s Laws of Motion 4. Newton’s Third Law of Motion states that when two bodies interact, they exert equal but opposite forces on each other. They are called action and reaction. 5. Action and reaction are equal in magnitude but opposite in direction. They act on different objects.

25. 24 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.2 Principle of Conservation of Linear Momentum 6. The total linear momentum of a system is constant, if there is no external forces acting on the system. 7. The Principle of Conservation of Linear Momentum and Newton’s Third Law of Motion are consistent with each other.

26. 25 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.3 Elastic and inelastic collisions 8. The most fundamental law in Physics is the Principle of Conservation of Energy, which states that the total energy of a closed system is conserved. 9. For elastic collisions, the total kinetic energy after collision is equal to that before collision. Therefore, kinetic energy, linear momentum and total energy are conserved.

27. 26 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.3 Elastic and inelastic collisions 10. For inelastic collisions without external force, kinetic energy is not conserved, but total energy and linear momentum are conserved.

28. 27 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.4 Inertial mass and gravitational mass 11. Inertial mass of a body is a measure of the reluctance to change its state. 12. Gravitational mass of a body is a measure of the gravitational attractive force acted on it (weight of the body).

29. 28 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.5 Conservation of momentum in two- dimension 13. If two equal masses collide obliquely, the angle between the two masses after collision would be 90 o.

30. 29 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.6 Work, energy and power 14. Work (W) = Fs cosθ where F and s are the magnitude of F and s respectively and θ is the angle between F and s. 15. Work is done by a force F to stretch a spring to produce an extension of e.

31. 30 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.6 Work, energy and power 16. The kinetic energy (K or KE) is the energy of a body due to its motion. 17. An object stores energy due to its physical condition or because of its position. The energy stored in the object is called potential energy (U or PE).

32. 31 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 137) 3.6 Work, energy and power

33. 32 © Manhattan Press (H.K.) Ltd. 3.6 Work, energy and power (SB p. 138)

34. 33 © Manhattan Press (H.K.) Ltd. End

35. 34 © Manhattan Press (H.K.) Ltd. A force does no work if: 1. There is no displacement. e.g. No work is done by static friction. 2. The displacement is perpendicular to the applied force. e.g. No work is done by gravitational force if one walks on a horizontal road. Return to Text 3.6 Work, energy and power (SB p. 125)

36. 35 © Manhattan Press (H.K.) Ltd. The sign of work The sign of work depends on the directions of force and displacement. 1. If their directions are the same, then positive work is done. 2. If their directions are opposite, then negative work is done. Take an example of lifting a box upwards. The lifting force does positive work since it is acted in the same direction as the displacement. However, the weight of the box does negative work since its direction is opposite to that of displacement. Return to Text 3.6 Work, energy and power (SB p. 126)

37. 36 © Manhattan Press (H.K.) Ltd. Q: Q:A sphere of mass m at the end of a string of length is released when the string is horizontal. The sphere then collides with a block of mass 4m at rests on a smooth table. If the collision is perfectly elastic, find in terms of m, and g, (a) the velocity of the sphere, and (b) the velocity of the block after collision. Solution 3.6 Work, energy and power (SB p. 131)

38. 37 © Manhattan Press (H.K.) Ltd. Solution: The velocity u of the sphere just before collision is given by: If v 1 = velocity of sphere and v 2 = velocity of block after collision, then using the Principle of Conservation of Momentum, mu = mv 1 + (4m)v 2 u = v 1 + 4v 2..........................(1) By conservation of kinetic energy: u 2 = v 1 2 + 4v 2 2.....................(2) Substituting (1) into (2), (v 1 + 4v 2 ) 2 = v 1 2 + 4v 2 2 v 1 2 + 8v 1 v 2 + 16v 2 2 = v 1 2 + 4v 2 2 4v 2 (3v 2 + 2v 1 ) = 0 3.6 Work, energy and power (SB p. 131) Substituting (3) into (1): Return to Text

39. 38 © Manhattan Press (H.K.) Ltd. Q: Q:(a) A ball bearing is released from a height of 1 m from a metal plate. Describe how you would determine the fractional decrease in the kinetic energy of the ball bearing after it hits the plate. What happens to the difference in kinetic energy? (b) A neutron of mass m collides head-on with a carbon nucleus of mass 12m which was initially at rest. If the collision is elastic, find the ratio of the kinetic energy of the neutron after collision to its kinetic energy before collision. Solution 3.6 Work, energy and power (SB p. 132)

40. 39 © Manhattan Press (H.K.) Ltd. Solution: (a) Suppose that the ball bearing is released from a height h o, and v o is the velocity of the ball bearing just before it hits the metal plate. Using the Principle of Conservation of Energy, Let v 1 = velocity of ball bearing immediately after collision, h 1 = height reached by it after collision. Using the Principle of Conservation of Energy, Therefore, the fractional decrease in kinetic energy: That is, the fractional decrease in kinetic energy is determined by measuring the heights h o and h 1 and substituting them into equation (3). The loss in kinetic energy is converted into heat and sound during collision. 3.6 Work, energy and power (SB p. 132)

41. 40 © Manhattan Press (H.K.) Ltd. Solution (cont’d): (b) Using the Principle of Conservation of Linear Momentum, mu 1 + 12m (0) = mv 1 + 12mv 2 u 1 = v 1 + 12v 2......................................... (1) Since the collision is elastic, kinetic energy of the system is conserved. substituting (1) into (2), (v 1 + 12v 2 ) 2 = v 1 2 + 12v 2 2 v 2 (132v 2 + 24v 1 ) = 0 3.6 Work, energy and power (SB p. 132)

42. 41 © Manhattan Press (H.K.) Ltd. Solution (cont’d): Return to Text 3.6 Work, energy and power (SB p. 132)

43. 42 © Manhattan Press (H.K.) Ltd. Q: Q:A toy car which is powered by a motor travels with constant velocity v. The figure shows the variation of the energy supplied by the motor with time t. If the constant force generated by the motor is F, find the value of v in terms of a, b, and F. (Neglect resistance to motion due to friction.) Solution 3.6 Work, energy and power (SB p. 134)

44. 43 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 3.6 Work, energy and power (SB p. 134)

45. 44 © Manhattan Press (H.K.) Ltd. Q: Q:A manufacturer claims that the maximum power delivered by the engine of a car of mass 1 200 kg is 90 kW. (a) Find the minimum time in which the car could accelerate from rest to 30 m s −1. (b) An independent test quotes that a time of 12 s is needed to accelerate the car from rest to 30 m s –1. Suggest a reason for the difference from the time you have calculated. Solution 3.6 Work, energy and power (SB p. 135)

46. 45 © Manhattan Press (H.K.) Ltd. Solution: (b) There is a difference in time because work is done to increase the kinetic energy of the car, and also work against friction. Return to Text 3.6 Work, energy and power (SB p. 135)