2. Momentum

4. Momentum and Collisions This chapter is concerned with inertia and motion. Momentum helps us understand collisions.

5. Momentum Inertia in motion mass => quantity of matter in an object inertia => an object's resistance to change in motion

6. Momentum Defined The quantity of motion, momentum, as being directly proportional to the object's mass and velocity. Momentum is a vector quantity……. ……..because it is a scalar (mass) of the vector velocity.

7. p = Mv

8. Momentum = mass X velocity

9. Momentum Defined  = m  v where  is momentum with units kg  m/s m is the mass with units kg v is the velocity with units m/s

10. Momentum Defined Very Fast objects have Greeeeat momentum Very Massive Objects have Greeeat momentum

11. Momentum If Direction Not Important……….. …….Momentum = mass x speed Therefore……..p = ms

12. A large truck has more momentum than a car moving at the same speed because it has a greater mass. Which is more difficult to slow down? The car or the large truck?

13. Large Momentum Examples: –Huge ship moving at a small velocity –High velocity bullet P = m v

14. Impulse In order to change the momentum of an object you must apply a force over some time interval. Impulse = Force  time interval  p= F  t

16. Impulse Newton’s Second Law can read  F = ma = m(  v/  t) = (  mv)/(  t) = (  p/  t) Rearranging, Impulse =  p = F  t

18. Impulse When force is limited... –increase  t (Follow through!) –make it bounce (Pelton wheel)

19. Impulse and Momentum Impulse = Change in Momentum = Final (mv) - Initial (mv) F  t = m  v

21. Make it Bounce p1p1 p 2 = -p 1  p = p 2 - p 1 = -p 1 - p 1 = -2p 1

22. Case 1: Increasing Momentum –Apply a force for a long time. –Examples: Follow through on a golf swing. Pushing a car. FtFt

23. Case 2: Decreasing Momentum –Apply a force for a long time. –Examples: Air bags in cars. Catching an egg. Boxing, Figure 5.6 Soft collisions, Figure 5.3. FtFt

24. Case 3: Decreasing Momentum –Apply a force for a short time. –Examples: Boxing Karate FtFt

25. Minimize the Force To minimize force … –Increase  t catching a ball Bungee jumping

26. If  F = 0, then impulse =  p = zero, or Momentum is conserved

27. Conservation of Momentum This means that the momentum doesn’t change. Recall that F t =  mv) In this equation, F is the "external force". Internal forces cannot cause a change in momentum.

28. Examples Conservation of Momentum: If there are no external forces, the total momentum for a system remains unchanged. Example 1: a person sitting inside a car pushing against the dashboard Example 2: a bullet fired from a rifle Example 3: a rocket is space

29. Conservation of Momentum

31. In any "closed system" the total momentum does not change.

32. Conservation of Momentum ……..(Total momentum) before event = (Total momentum) after event (m b v b + m r v r ) before = (m b v b + m r v r ) after

33. Demonstrations Rocket balloon Cannon Rocket Scooter

34. When can Momentum be Conserved? u Internal forces cannot cause a change in momentum of the system. u For conservation of momentum, the external forces must be zero.

35. Momentum and Collisions Elastic Collisions –objects rebound –e.g. superball Inelastic Collisions –object stick together an usually become distorted and generate heat –e.g. clay ball

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

37. v = 10v = 0 Before Collision MM p = Mv MM After Collision p = 2Mv’ Mv = 2Mv’ v’ = ½ v v’ = 5

38. Conserve Energy and Momentum Case 1: Case 2: Equal masses M > M Case 3: M < M Before Collision

39. Momentum = Mass x Velocity p = mv

40. v

41. Elastic and inelastic collision

42. MM M M V1V2 V1’ V2’ Before Collision After Collision

46. Types of Collisions 1. Elastic 2. Inelastic collisions 3. Completely Inelastic collisions

47. Elastic Collisions Momentum…. is conserved in every collision Kinetic Energy…..is conserved……. …..No sound or heat is produced

49. Elastic Collisions Examples….. Subatomic particles repelling magnets a “perfect”super ball

50. Elastic Collisions M 1 v 1o + m 2 v 2o = m 1 v 1f +m 2 v 2f

51. Inelastic Collisions Momentum…... is conserved Kinetic Energy……. is not conserved lost in form of heat or sound Contains almost all types of collisions

52. Inelastic Collisions M 1 v 1o + m 2 v 2o = (m 1 +m 2 )v f

53. Perfectly Inelastic Collisions More…. Kinetic energy is lost as heat or sound Colliding objects stick together

58. Example Problems...