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Collisions

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

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Collisions

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  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

  7. © D Hoult 2010

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

  9. A B vB After collision, the total momentum is equal to the momentum of body B © 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) mAuA = mBvB © 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) mAuA = mBvB 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) mAuA = mBvB 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. A B © D Hoult 2010

  16. A B uA © D Hoult 2010

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

  18. A B vA vB © D Hoult 2010

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

  20. If we want to calculate the velocities, vA and vB we will use the A B vA vB © D Hoult 2010

  21. If we want to calculate the velocities, vA and vB we will use the principle of conservation of momentum A B vA vB © D Hoult 2010

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

  23. The principle of conservation of momentum can be stated here as mAuA = mAvA + mBvB © D Hoult 2010

  24. The principle of conservation of momentum can be stated here as mAuA = mAvA + mBvB If the collision is elastic then © D Hoult 2010

  25. The principle of conservation of momentum can be stated here as mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved © D Hoult 2010

  26. The principle of conservation of momentum can be stated here as mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved ½mAuA2 = ½mAvA2+ ½mBvB2 © D Hoult 2010

  27. The principle of conservation of momentum can be stated here as mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved ½mAuA2 = ½mAvA2+ ½mBvB2 mAuA2 = mAvA2+ mBvB2 © D Hoult 2010

  28. mAuA = mAvA + mBvB mAuA2 = mAvA2+ mBvB2 From these two equations, vA and vB can be found © D Hoult 2010

  29. mAuA = mAvA + mBvB mAuA2 = mAvA2+ mBvB2 From these two equations, vA and vB can be found BUT © D Hoult 2010

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

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

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

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

  35. It can be shown* that for an elastic collision, the velocity of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision vA vB and the velocity of B relative to A after the collision is equal to vB – vA © D Hoult 2010

  36. It can be shown* that for an elastic collision, the velocity of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision vA vB and the velocity of B relative to A after the collision is equal to vB – vA for proof click here © 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 mAuA = mAvA + mBvB equation 2 © 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 mAuA = mAvA + mBvB equation 2 uA = vB – vA © D Hoult 2010

  40. © D Hoult 2010

  41. © D Hoult 2010

  42. A B uA © D Hoult 2010

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

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

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

  46. Using the principle of conservation of momentum mAuA = mAvA + mBvB © D Hoult 2010

  47. Using the principle of conservation of momentum mAuA = mAvA + mBvB A B vA vB © D Hoult 2010

  48. Using the principle of conservation of momentum mAuA = mAvA + mBvB A B vA vB © D Hoult 2010

  49. Using the principle of conservation of momentum mAuA = mAvA + mBvB A B vA vB One of the momenta after collision will be a negative quantity © D Hoult 2010

  50. 2 dimensional collision © D Hoult 2010

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