3. Chapter 8 Impulse and Momentum

4. THE LINEAR MOMENTUM  Momentum = mass times velocity  “Think of it as inertia in motion” Units - kg m/s or sl ft/s

5. AN IMPULSE  Collisions involve forces (there is a  v).  Impulse = force times time. Units - N s or lb s

6. AN IMPULSE CAUSES A CHANGE MOMENTUM Impulse = change in momentum

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

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

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

11. BOUNCING There is a greater impulse with bouncing. Example: Pelton Wheel Pelton Wheel Water Sprinkler

12. l Consider a hard ball and a clay ball that have +10 units of momentum each just before hitting a wall. l The clay ball sticks to the wall and the hard ball bounces off with -5 units of momentum. l Which delivered the most “punch” to the wall?

13. Initial momentum of the clay ball is 10. Final momentum of clay ball is 0. The change is 0 - 10 = - 10. It received - 10 impulse so it applied + 10 to the wall.

14. Initial momentum of the hard ball is 10. Final momentum of hard ball is - 5. The change is - 5 - 10 = - 15. It received - 15 impulse so it applied + 15 to the wall.

15. Example: Rifle and bullet Demo - Rocket balloon Demo - Clackers Video - Cannon Shoot Video – Scooter Propulsion CONSERVATION OF LINEAR MOMENTUM

16. IN COLISIONS AND EXPLOSIONS

17. 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

18. In one dimension in component form,

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

20. IN COLLISIONS AND EXPLOSIONS  Collisions involve forces internal to colliding bodies.  Inelastic collisions - conserve momentum  Totally inelastic collisions - conserve momentum and objects stick together

21. A PERFECTLY ELASTIC COLLISION  Perfectly elastic collisions - conserve energy and momentum

22. Demos  Demo - Momentum balls  Demo - Small ball/large ball drop  Demo - Funny Balls

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

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

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

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

28.   Your danger is of the order of twenty times greater than that of the truck driver. TRUCKS.  Don’t mess with T

29. COEFFICIENT OF RESTITUTION For any collision between two bodies moving along a single straight line, the coefficient of restitution e is defined as

30. u’s are velocities before impact. v’s are velocities after impact. For perfectly elastic collisions e = 1. For inelastic collisions e < 1. For totally inelastic collisions e = 0.

31. 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)

32. Collision between two objects of the same mass. One mass is at rest. Example of Non-Head-On Collisions (Energy and Momentum are Both Conserved) If you vector add the total momentum after collision, you get the total momentum before collision.

33. THE CENTER OF MASS The center of mass of an object of mass m is the single point that moves in the same way as a point mass would move when subjected to the same external forces that act on the object.

34. The coordinates of the center of mass are

35. . CENTER OF MASS AND CENTER OF GRAVITY Center of mass - average position of mass Earth. Center of gravity - average position of weight

36. Path of center of mass of a rotating object will be a straight line if no external forces act on the object.

37. Locating the Center of Gravity  Demo - Meterstick  Demo - Map of Texas  Demo - Balancing eagle  Demo - Curious George Center can be outside of the object. Examples: high jump and pole vaulting