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Conservation of momentum

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Conservation of momentum

## Conservation of momentum

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1. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob = mava + mbvb • mavoa + mbvob = (ma + mb)vab

2. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob = mava + mbvb • mavoa + mbvob = (ma + mb)vab

3. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob = mava + mbvb • mavoa + mbvob = (ma + mb)vab

4. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob = mava + mbvb • mavoa + mbvob = (ma + mb)vab

5. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob= mava + mbvb • mavoa + mbvob = (ma + mb)vab

6. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob= mava + mbvb • mavoa + mbvob = (ma + mb)vab

7. Conservation of momentum • Momentum before = momentum after • po = p • mavoa + mbvob= mava + mbvb • mavoa + mbvob = (ma + mb)vab

8. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

9. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

10. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

11. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

12. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

13. 7 Collisions Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collision po = p and KEo=KE for magnetic bumper collisions mbc voc + mrc vorc = mbc vbc + mrc vrc ½ mbc voc2 + ½ mrc vorc2 = ½ mbc vbc2 + ½ mrc vrc2 Elastic Collisions

14. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p and KEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

15. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p and KEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

16. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p andKEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

17. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p andKEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

18. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p andKEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

19. 7 Collision Lab • 7 collisions – inelastic and elastic collisions Blue cart red cart collisions po = p andKEo=KE for velcro collision mbc voc + mrc vorc = ( mbc + mrc ) vbrc ½ mbc voc2 + ½ mrc vorc2 > ½ (mbc + mrc)vrc2 Inelastic Collisions

20. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

21. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

22. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

23. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

24. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

25. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

26. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

27. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

28. Ballistic Pendulum • Momentum • p before = p after • mb vob = ( mb + mp ) vbp • vob = ( mb + mp ) vbp • mb • Kinetic Energy = Gravitational Potential • ½ (mb + mp) vbp2 = (mb + mp ) gh • ½ vbp2 = gh • vbp2 = 2gh • vbp = 2gh • Therefore vob = (mb+mp) 2gh • mb

29. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

30. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

31. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

32. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

33. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

34. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

35. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

36. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

37. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

38. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

39. Ballistic Sled • Momentum • p before = p after • mb vob = ( mb + ms ) vbs • vob = ( mb + ms ) vbs • mb • Kinetic Energy = Work done against friction • ½ (mb + ms) vbs2 = Wfr • ½ (mb + ms) vbs2 = Ffr d • ½ (mb + ms) vbs2 = mFN d • ½ (mb + ms) vbs2 = m(mb + ms) gd • ½ vbs2 = mgd • Vbs = 2 mgd Therefore vob = (mb+ms) 2mgd • mb

40. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

41. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

42. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

43. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

44. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

45. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

46. Off Center Collision Overall momentum before = overall momentum after Horizontal momentum before = Horizontal momentum after Vertical momentum before = vertical momentum after p0 = p pox = px poy = py mwb vowbx + mbb vobbx = mwb vwbx + mbb vbbx mwb vowby + mbb vobby = mwb vwby + mbb vbby

47. Collision and Impulse

48. Collision and Impulse Impulse = ½ b h = ½ t F F t