1. Electrical potential energy q is the charge ( 电荷 ) on each object r is the distance between the two objects

2. Your turn…

3. Binding energy

4. Total energy of an oxygen molecule (O 2 ): Some of the mass disappears in the chemical reaction! (It was carried away by a photon.) This is the binding energy of the molecule (around 5 eV for O 2 ). Bound system

5. Example: Nuclear fusion alpha particlecarbon (C) nucleus excited oxygen (O) nucleus alpha and C touch O nucleus and photon M&I Chap 6, pp 269-271

6. The force generated by this spring, stretched a distance x, is: where k is the stiffness. So the potential energy is given by: Potential energy of a spring ( 弹簧 )

7. Your turn…

8. This is only true when s is not very large. Of course, when s approaches infinity (∞), the spring will break! Potential energy of a spring ( 弹簧 )

9. Example: Bungee jumping Dave (m = 75 kg) jumps off a bridge with a bungee cord (k = 50 N/m) tied to his feet. He falls for 15 meters before the cord begins to stretch. How far will he fall before he stops?

10. Example: Initial Final Cord starts stretching System: Dave + cord + Earth Surroundings: none Final state: Cord stretched, Dave hanging under the bridge, at rest y h s 15 m y = 0 Initial state: Dave on top of bridge, at rest

11. Example: Initial Final Cord starts stretching Energy principle: No work done on system, so y h s 15 m y = 0

12. What is the maximum height reached by the block after it bounces? Potential energy changes are path independent.

13. Initial Final

14. Initial Final The change in potential energy does not depend on the path taken.

15. InitialFinal Moving in a loop ( 闭合路径 ) causes no change in potential energy.

16. Forces that have a potential energy are called conservative forces ( 保守力 )

17. What about friction?

18. The interaction does not depend on position; it depends on the direction of the velocity. Therefore, it is not a conservative force. So there is no potential energy associated with friction.

19. ΔxΔx Block and table both heat up. Kinetic energy is converted to thermal energy ( 热能 ).

20. ΔxΔx The total change in energy over the return trip is not zero. Kinetic energy was lost to heat both times.

21. We cannot calculate the work done by the table on the block. All we know is the change in thermal energy ΔE thermal of the (block + table) system.

22. Energy Principle for systems with internal friction where Important: This is not the work of one object on the other. It is the change in thermal energy of the whole system.

23. Air drag and fluid drag are also non-conservative forces. Object falling through fluid:

24. Air drag and fluid drag are also non-conservative forces. Object falling through air: In both cases,

25. Example: Skiing, with friction θ θ L System: Skier + hill + Earth Surroundings: none Final state: Skier moving at base of hill; skis and hill a bit hotter Initial state: Skier on top of hill, at rest h μ k = 0.090

26. Example: Skiing, with friction Energy principle: No work done on system, so

27. Power: energy per unit time instantaneous power Units: J/s or watts (W) M&I Ch 7, p 304 功率

28. Rotational energy M&I Chapter 9

29. Center of mass 质量中心

30. x y 2.0 m Example CM Two particles with the same mass m. mass = m

31. x y 2.0 m Example What if one of the particles has 3 times the mass of the other? mass = mmass = 3m

32. x y 2.0 m Example The COM moves closer to the more massive particle. mass = mmass = 3m CM

33. x y 2.00 m 1.5 m Example CM Three particles with the same mass m.

34. Now, differentiate this equation with respect to time :

35. (assuming… what?) Total momentum

36. Momentum principle:

38. VPython program: translation and rotation

39. Your turn…

42. Separation of kinetic energy [For solid objects ( 刚体 ), we assume no vibration.]

43. Angular speed A rigid body, rotating with constant period T around a fixed axis.

44. Angular speed Greek letter omega 弧度

46. where r is the distance to the axis of rotation.

47. Rotational kinetic energy

51. Moment of inertia, I

53. where is the moment of inertia ( 转动惯量 ), which depends on the distribution of mass in the object.

54. Your turn…

56. Moment of inertia of a bicycle wheel Assume that all the atoms in the wheel are the same distance R from the center. Let m be the mass of each atom. Then

57. Your turn…

58. Example How much work do you do? Chap 9, p 356

59. Example: Moment of inertia of a thin rod Mass of each piece:

60. Example: Moment of inertia of a thin rod Moment of inertia of each piece:

61. Example: Moment of inertia of a thin rod Total moment of inertia:

62. Example: Moment of inertia of a thin rod Total moment of inertia:

63. Example: Moment of inertia of a thin rod Total moment of inertia:

64. Moments of inertia have been calculated for many different shapes. No need to memorize them all! Just remember the definition of I.

65. Total kinetic energy

66. Rotation around a point not at the center of mass

67. Parallel axis theorem Rotation around a point not at the center of mass

68. Which will hit the floor first? (1) Bare stick (2) Stick + brick (3) Both at the same time