1. Worksheet 1: Due next lecture Put it on the desk at the beginning of class Late: Same day -20% Before start of next lecture -50% Any later -100%

2. Newton’s first law is only qualitative: we can’t use it calculate anything. 定性的

3. We need a quantitative law of motion, one we can use to predict the future. 定量的

4. Newton’s Second Law of Motion The change in momentum of a system is equal to the net force acting on the system times the duration of the interaction.

5. Newton’s Second Law of Motion (Momentum Principle) (Assumes force is constant during time Δt.)

6. Newton’s Second Law of Motion (Momentum Principle) Impulse 冲量

7. Newton’s Second Law of Motion (Momentum Principle) Impulse 冲量

8. Newton’s Second Law of Motion The change in momentum of a system is equal to the net impulse acting on the system.

9. y x Consider Δp, the change in the ball’s momentum. Is Δp x positive, negative, or zero?

10. y x Consider Δp, the change in the ball’s momentum. Is Δp y positive, negative, or zero?

11. y x Consider Δp, the change in the ball’s momentum. What is the direction of Δp?

12. Force has units of Newtons (N). 1 N is roughly the gravitational force on a small apple.

13. Example A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction. (a) What impulse acts on the ball while it is in contact with the bat?

14. Example A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction. (a) What impulse acts on the ball while it is in contact with the bat?

15. Example A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction. (b) The impact time Δt for the collision is 1.2 ms. What average force does the bat apply to the ball?

16. Jumping up and down (1)Land on your toes, with bent knees – Δt is large, so F is small. (2)Land on your heels, with locked knees – Δt is small, so F is large (and it hurts!)

17. F t ΔtΔt Area of the rectangle is the impulse

18. F t ΔtΔt Area under the curve is the impulse What if the force changes during the time Δt?

19. F avg t ΔtΔt Average force:

20. Your turn…

21. Important: F x can only change p x. F y can only change p y. F z can only change p z.

22. Your turn…

26. First, let’s re-arrange: Assuming v << c, we can use :

27. Newton’s Second Law of Motion (alternative version) This version is less fundamental than the first one. It is only true for v << c.

28. Predicting the future

29. “stiffness”

31. The stretch s: The vector spring force:

32. Your turn…

33. A spring whose stiffness is 30 N/m is 12 cm (0.12 m) long when relaxed. You push on the spring, compressing it so its length is now 10 cm (0.10 m). What is the stretch s ? 1) 0.02 m 2) 0.12 m 3) 0.10 m 4) −0.02 m 5) −0.12 m 6) −0.10 m Your turn…

35. m = 0.06 kg k s = 8 N/m L = 0.1 m Predict the motion of the block during the first 0.3 s after it is released.

36. Iterative prediction of motion 迭代 Calculate all acting on the system Apply momentum principle: Find new position of system:

37. Step 1 (t = 0.1 s)

38. Your turn…

39. Step 2 (t = 0.2 s)

40. Step 3 (t = 0.3 s)

41. After 3 time steps…

42. After 10 time steps…

43. With a much smaller time step (Δt = 0.01 s) …