1. Impulse 冲量

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

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

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

5. This is called impulse, J. It has the same units as momentum.

6. Another way of writing Newton’s 2 nd Law:

7. 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?

8. 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?

9. 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?

10. An ice hockey puck ( 冰球 ) has an initial momentum of kg m/s. It slides across the ice, slowing down, until it stops. What was the impulse applied by the ice to the puck? (1) kg m/s (4) kg m/s (2) kg m/s (5) kg m/s (3) kg m/s

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

12. F t ΔtΔt Area of the rectangle is J

13. F t ΔtΔt Area under the curve is J What if the force changes during the time Δ t?

14. F avg t ΔtΔt Average force:

15. Systems of many particles System Environment We can still use Newton’s 2 nd Law on systems of more than one particle. We just need to be careful about the difference between internal forces ( 内力 ) and external forces ( 外力 ).

16. Systems of many particles System Environment Internal forces are interactions between particles within the system. External forces are interactions between the system and the environment.

17. Systems of many particles System Environment Only external forces count towards the net force F net in Newton’s 2 nd Law. External forces only!

18. What if there are no external forces on a system: F net = 0?

19. The total momentum doesn’t change.

20. Conservation of momentum 动量守恒

22. Example BeforeAfter y x Find the speeds of the balls after the collision. v 1 = 3.0 m/s