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Conservation of momentum

Conservation of momentum. Momentum before = momentum after p o = p m a v oa + m b v ob = m a v a + m b v b m a v oa + m b v ob = (m a + m b ) v ab. Conservation of momentum. Momentum before = momentum after p o = p m a v oa + m b v ob = m a v a + m b v b

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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 F

  49. Collision and Impulse F t

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

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