1. Collisions © D Hoult 2010

2. Elastic Collisions © D Hoult 2010

3. Elastic Collisions 1 dimensional collision © D Hoult 2010

4. Elastic Collisions 1 dimensional collision: bodies of equal mass © D Hoult 2010

5. Elastic Collisions 1 dimensional collision: bodies of equal mass (one body initially stationary) © D Hoult 2010

6. Elastic Collisions 1 dimensional collision: bodies of equal mass (one body initially stationary) © D Hoult 2010

8. Before collision, the total momentum is equal to the momentum of body A AB uAuA © D Hoult 2010

9. After collision, the total momentum is equal to the momentum of body B AB vBvB © D Hoult 2010

10. The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies) © D Hoult 2010

11. The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies) m A u A = m B v B © D Hoult 2010

12. The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies) m A u A = m B v B so, if the masses are equal the velocity of B after © D Hoult 2010

13. The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies) m A u A = m B v B so, if the masses are equal the velocity of B after is equal to the velocity of A before © D Hoult 2010

14. Bodies of different mass © D Hoult 2010

15. AB

16. AB uAuA

17. AB uAuA Before the collision, the total momentum is equal to the momentum of body A © D Hoult 2010

18. AB vAvA vBvB

19. AB vAvA vBvB After the collision, the total momentum is the sum of the momenta of body A and body B © D Hoult 2010

20. AB vAvA vBvB If we want to calculate the velocities, v A and v B we will use the © D Hoult 2010

21. AB vAvA vBvB If we want to calculate the velocities, v A and v B we will use the principle of conservation of momentum © D Hoult 2010

22. The principle of conservation of momentum can be stated here as © D Hoult 2010

23. m A u A = m A v A + m B v B The principle of conservation of momentum can be stated here as © D Hoult 2010

24. m A u A = m A v A + m B v B If the collision is elastic then The principle of conservation of momentum can be stated here as © D Hoult 2010

25. m A u A = m A v A + m B v B If the collision is elastic then kinetic energy is also conserved The principle of conservation of momentum can be stated here as © D Hoult 2010

26. m A u A = m A v A + m B v B If the collision is elastic then kinetic energy is also conserved ½ m A u A 2 = ½ m A v A 2 + ½ m B v B 2 The principle of conservation of momentum can be stated here as © D Hoult 2010

27. m A u A = m A v A + m B v B If the collision is elastic then kinetic energy is also conserved m A u A 2 = m A v A 2 + m B v B 2 ½ m A u A 2 = ½ m A v A 2 + ½ m B v B 2 The principle of conservation of momentum can be stated here as © D Hoult 2010

28. From these two equations, v A and v B can be found m A u A = m A v A + m B v B m A u A 2 = m A v A 2 + m B v B 2 © D Hoult 2010

29. From these two equations, v A and v B can be found m A u A = m A v A + m B v B m A u A 2 = m A v A 2 + m B v B 2 BUT © D Hoult 2010

30. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision © D Hoult 2010

31. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision * a very useful phrase ! © D Hoult 2010

32. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision In this case, the velocity of A relative to B, before the collision is equal to uAuA © D Hoult 2010

33. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision In this case, the velocity of A relative to B, before the collision is equal to u A uAuA © D Hoult 2010

34. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision and the velocity of B relative to A after the collision is equal to vAvA vBvB © D Hoult 2010

35. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision and the velocity of B relative to A after the collision is equal to v B – v A vAvA vBvB © D Hoult 2010

36. It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision for proof click hereclick here and the velocity of B relative to A after the collision is equal to v B – v A vAvA vBvB © D Hoult 2010

37. We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 © D Hoult 2010

38. We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 equation 2 m A u A = m A v A + m B v B © D Hoult 2010

39. We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 equation 2 m A u A = m A v A + m B v B u A = v B – v A © D Hoult 2010

42. AB uAuA

43. Before the collision, the total momentum is equal to the momentum of body A AB uAuA © D Hoult 2010

44. After the collision, the total momentum is the sum of the momenta of body A and body B AB vAvA vBvB © D Hoult 2010

45. Using the principle of conservation of momentum © D Hoult 2010

46. Using the principle of conservation of momentum m A u A = m A v A + m B v B © D Hoult 2010

47. Using the principle of conservation of momentum m A u A = m A v A + m B v B AB vAvA vBvB © D Hoult 2010

48. Using the principle of conservation of momentum m A u A = m A v A + m B v B AB vAvA vBvB © D Hoult 2010

49. Using the principle of conservation of momentum m A u A = m A v A + m B v B AB vAvA vBvB One of the momenta after collision will be a negative quantity © D Hoult 2010

50. 2 dimensional collision © D Hoult 2010

51. 2 dimensional collision © D Hoult 2010

53. A B

54. A B Before the collision, the total momentum is equal to the momentum of body A © D Hoult 2010

56. After the collision, the total momentum is equal to the sum of the momenta of both bodies © D Hoult 2010

57. Now the sum must be a vector sum © D Hoult 2010

58. mAvAmAvA

59. mBvBmBvB mAvAmAvA

60. mBvBmBvB mAvAmAvA

61. mBvBmBvB mAvAmAvA

62. mBvBmBvB mAvAmAvA

63. p mBvBmBvB mAvAmAvA

64. mBvBmBvB mAvAmAvA p mAuAmAuA

65. mBvBmBvB mAvAmAvA p mAuAmAuA

66. mBvBmBvB mAvAmAvA p mAuAmAuA

67. p =mAuAmAuA mBvBmBvB mAvAmAvA p mAuAmAuA © D Hoult 2010

68. 2 dimensional collision: Example Body A has initial speed u A = 50 ms -1 © D Hoult 2010

69. 2 dimensional collision: Example Body A has initial speed u A = 50 ms -1 Body B is initially stationary © D Hoult 2010

70. 2 dimensional collision: Example Body A has initial speed u A = 50 ms -1 Body B is initially stationary Mass of A = mass of B = 2 kg © D Hoult 2010

71. 2 dimensional collision: Example Body A has initial speed u A = 50 ms -1 Body B is initially stationary Mass of A = mass of B = 2 kg After the collision, body A is found to be moving at speed v A = 25 ms -1 in a direction at 60° to its original direction of motion © D Hoult 2010

72. 2 dimensional collision: Example Body A has initial speed u A = 50 ms -1 Body B is initially stationary Mass of A = mass of B = 2 kg After the collision, body A is found to be moving at speed v A = 25 ms -1 in a direction at 60° to its original direction of motion Find the kinetic energy possessed by body B after the collision © D Hoult 2010