2. 1.MOMENTUM l Momentum = mass times velocity Units - kg m/s

3. 2.IMPULSE Collisions involve forces (there is a  v). l Impulse = force times time. Units - N s

4. 3.IMPULSE CHANGES MOMENTUM Impulse = change in momentum

6. Case 1 Increasing Momentum Follow through Examples: Long Cannons Driving a golf ball Can you think of others?

7. Case 2 Decreasing Momentum over a Long Time Examples: Bungee Jumping Can you think of others? Warning – May be dangerous

8. Case 3 Decreasing Momentum over a Short Time Examples: Boxing (leaning into punch) Head-on collisions Can you think of others?

9. 5. CONSERVATION OF MOMENTUM Example: Rifle and bullet Demo - Rocket balloon Demo - Clackers Video - Cannon recoil Video - Rocket scooter

10. Consider two objects, 1 and 2, and assume that no external forces are acting on the system composed of these two particles. Impulse applied to object 1 Impulse applied to object 2 Total impulse applied to system or Apply Newton’s Third Law

11. l Internal forces cannot cause a change in momentum of the system. l For conservation of momentum, the external forces must be zero.

12. 6.COLLISIONS  Collisions involve forces internal to colliding bodies.  Elastic collisions - conserve energy and momentum  Inelastic collisions - conserve momentum  Totally inelastic collisions - conserve momentum and objects stick together

13. Elastic and Inelastic Collisions l In an elastic collision the total kinetic energy is conserved n Momentum is conserved in any collision n Example: n What are signs of final velocities?

14. Elastic and Inelastic Collisions n Example (cont.): n Consider reference frame where CM is at rest

15. Elastic and Inelastic Collisions l In an inelastic collision the total kinetic energy is not conserved n Momentum is conserved in any collision n Example: case where particles stick together

16. Elastic and Inelastic Collisions l Example: Ballistic Pendulum

17. Collision between two objects of the same mass. One mass is at rest. Collision between two objects. One not at rest initially has twice the mass. Collision between two objects. One at rest initially has twice the mass. Simple Examples of Head-On Collisions (Energy and Momentum are Both Conserved)

18. Head-On Totally Inelastic Collision Example l Let the mass of the truck be 20 times the mass of the car. l Using conservation of momentum, we get

19. initial momentum of system = final momentum of system

20. l Remember that the car and the truck exert equal but oppositely directed forces upon each other. l What about the drivers? l The truck driver undergoes the same acceleration as the truck, that is

21. l The car driver undergoes the same acceleration as the car, that is The ratio of the magnitudes of these two accelerations is

22. Remember to use Newton’s Second Law to see the forces involved. l For the truck driver his mass times his acceleration gives For the car driver his mass times his greater acceleration gives

23. , big trucks that is. l l Your danger is of the order of twenty times greater than that of the truck driver. TRUCKS l Don’t mess with T

24. Collisions in 2D l Use Conservation of Momentum in each direction n Consider case where one particle is at rest n In CM frame particles are back-to-back!

25. Rocket Propulsion l “Rockets can’t fly in vacuum. What do they have to push against?” n Nonsense. Rockets don’t push; they conserve momentum, and send parts (fuel) away from the body as fast as possible

26. Rocket Propulsion l How fast do rockets accelerate? Start at rest, with mass M+  m Some time  t later, have expelled  m at speed v e, to conserve momentum, rest of rocket (M) must have velocity (in the other direction) of  v = v e  m/M

27. Rocket Propulsion l How fast do rockets accelerate? l Thrust: (instantaneous) force on rocket