Work and Potential Energy

1. Work and Potential Energy

2. We had earlier looked briefly at describing potential energy and more substantially at kinetic energy.

3. We had earlier looked briefly at describing potential energy and more substantially at kinetic energy. • We will again briefly look at potential energy.

4. When an object is thrown upward negative work is done by the gravitational force. +W -W

5. When an object is thrown upward negative work is done by the gravitational force. • As the object rises kinetic energy is is transferred to PE. As a result the object slows and eventually stops some height h. +W -W

6. However as the object falls positive work is done by the gravitational force. +W -W

7. However as the object falls positive work is done by the gravitational force. • As the object falls the potential energy is converted to kinetic energy. +W -W

8. However as the object falls positive work is done by the gravitational force. • As the object falls the potential energy is converted to kinetic energy. • In each case, the change in PE is equal to the negative work. +W -W

9. In the previous example, the direction of the energy transfer for a path is reversed for the path of the opposite direction.

10. In the previous example, the direction of the energy transfer for a path is reversed for the path of the opposite direction. • The force acting on the object is an example of a conservative force.

11. Conservative Forces

12. The net work done by a conservative force on a particle moving around a closed path is zero. 1 b a 2

13. The work done by a conservative force on a particle in moving between two points is independent of the path taken by the particle. 1 b a 2

14. For a conservative force when the system configuration changes, the force does work. • When the configuration change is reversed, the force reverses the energy transfer. The system in the initial example is the object and the Earth. The force doing the work is the gravitational force.

15. The gravitational, elastic and electric forces are examples of conservative forces.

16. A block of mass 2kg slides down a frictionless track as show below. If the block travel a total distance of 2.0m through a vertical displacement of 0.80m, how much work is done by the gravitational force?

17. d • A block of mass 2kg slides down a frictionless track as show below. If the block travel a total distance of 2.0m through a vertical displacement of 0.80m, how much work is done by the gravitational force? h

18. d • The work done is given by, θ is the angle between the force and the displacement h

19. d • The work done is given by, θ is the angle between the force and the displacement h

20. d • Similarly, h

21. d • Similarly, • Total work, h

22. Deriving the expression for Potential energy Gravitational PE & Elastic PE

23. Work done,

24. Work done, • Therefore,

25. Work done, • Therefore, • For the gravitational potential energy,

26. Work done, • Therefore, • For the gravitational potential energy,

27. Work done, • Therefore, • For the gravitational potential energy,

28. Work done, • Therefore, • For the gravitational potential energy,

29. Therefore,

30. Therefore, • Taking our reference to be zero,

31. For an elastic system (eg. Spring-block system)

32. For an elastic system (eg. Spring-block system)

33. For an elastic system (eg. Spring-block system)

34. For an elastic system (eg. Spring-block system) • Using initial conditions, (elastic potential energy)

35. Conservation of Mechanical energy

36. The mechanical energy Emec of a system is the sum of the potential and kinetic energy.

37. The mechanical energy Emec of a system is the sum of the potential and kinetic energy. • For an isolated system, when a conservative force does work W on an object energy is transferred between the kinetic and potential energy.

38. The mechanical energy Emec of a system is the sum of the potential and kinetic energy. • For an isolated system, when a conservative force does work W on an object energy is transferred between the kinetic and potential energy. • The change in KE is,

39. The change in PE is,

40. The change in PE is, • Therefore,

41. The change in PE is, • Therefore, • And, (conservation of mechanical energy)

42. The change in PE is, • Therefore, • And, • Equivalently, (conservation of mechanical energy)

43. The work done by and external force & Conservation of energy

44. So far we have looked at cases where there is no friction or external forces. • When an external force acts on a system energy is transferred by the force to or from the system.

45. So far we have looked at cases where there is no friction or external forces. • When an external force acts on a system energy is transferred by the force to or from the system. • When energy is transferred to the system, the work done is positive. • Negative work is done when energy is lost.

46. Consider the simple case of throwing a ball upward (ignoring friction).

47. Consider the simple case of throwing a ball upward (ignoring friction). • During the upward motion of the hand a force is applied to the ball (by your hand).

48. Consider the simple case of throwing a ball upward (ignoring friction). • During the upward motion of the hand a force is applied to the ball (by your hand). • This work is used to change the kinetic and potential energy of the ball. The velocity of the ball and hence KE increases. At the same time the height of the ball wrt the ground and hence the PE changes.

49. From definition, the work done by the external force produces the change in PE and KE.

50. From definition, the work done by the external force produces the change in PE and KE.