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Linear Momentum

Linear Momentum. is the product of mass times velocity m v. IMPULSE. Impulse is the product of the net Force and the time of contact. IMPULSE = F NET t. IMPULSE-MOMENTUM. The net Force produces acceleration. we wish to show that Impulse produces momentum.

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Linear Momentum

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  1. Linear Momentum is the product of mass times velocity m v

  2. IMPULSE Impulse is the product of the net Force and the time of contact. IMPULSE = FNETt

  3. IMPULSE-MOMENTUM The net Force produces acceleration. we wish to show that Impulse produces momentum.

  4. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a

  5. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET

  6. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv D t

  7. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t

  8. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t Then FNET D t = m D v

  9. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t Then FNET D t = m D v = D(m v)

  10. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t Then FNET D t = m D v = D(m v) So Impulse =FNET D t

  11. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t Then FNET D t = m D v = D(m v) So Impulse =FNET D t D(m v) = Change in Momentum

  12. Derivation of Impulse -Momentum from Newton’s Second Law FNET = m a Substitute for a in FNET where a = Dv so FNET = mD v D t D t Then FNET D t = m D v = D(m v) So Impulse =FNET D t =D(m v) = Change in Momentum

  13. CONSERVATION Conservation in Physics means that a quantity’s value does not change after certain physical processes.

  14. CONSERVATION Conservation in Physics means that a quantity’s value does not change after certain physical processes. That is:the value of the quantity is the same before and after the process. What are the quantity’s which are conserved?

  15. CONSERVED QUANTITIES Linear Momentum Angular Momentum

  16. CONSERVED QUANTITIES Linear Momentum Angular Momentum Total Energy Charge

  17. CONSERVED QUANTITIES Linear Momentum Angular Momentum Total Energy Charge And in special cases: mechanical energy mass volume

  18. CONSERVED QUANTITIES Linear Momentum Angular Momentum Total Energy Charge And in special cases: mechanical energy mass volume For elementary particles one finds that quantitites: such as parity, spin, charge, baryon number, charm, color, upness, downness and strangeness are conserved.

  19. Conserving Processes For Impulse and Momentum the conserving process is a collision between two or more objects.

  20. Conserving Processes For Impulse and Momentum the conserving process is a collision between two or more objects. For energy the conserving process is measuring the energy at one time and comparing it with the value at a later time.

  21. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B = - FNET B on A

  22. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B D t = - FNET B on A D t

  23. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B D t = - FNET B on A D t From Impulse Momentum Equation then D(m v)A on B = - D(m v)B on A

  24. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B D t = - FNET B on A D t From Impulse Momentum Equation then D(m v)A on B = - D(m v)B on A The left side mAvbefore - mA vafter

  25. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B D t = - FNET B on A D t From Impulse Momentum Equation then D(m v)A on B = - D(m v)B on A The left side mAvbefore - mA vafter The right side mBvafter - mB vbefore

  26. Derivation for the Law of Conservation of Momentum Newton’s Third Law of Action and Reaction FNETA on B D t = - FNET B on A D t From Impulse Momentum Equation then D(m v)A on B = - D(m v)B on A The left side mAvbefore - mA vafter The right side mBvafter - mB vbefore Thus mAvbefore + mB vbefore = mA vafter + mBvafter

  27. Example of Momentum Conservation A 50 kg boy on roller skates moving with a speed of 5 m/s runs into a 40 kg girl also on skates. After the collision they cling together. What is their speed? G U

  28. Example of Momentum Conservation A 50 kg boy on roller skates moving with a speed of 5 m/s runs into a 40 kg girl also on skates. After the collision they cling together. What is their speed? G mb = 50 kg vb = 5 m/s U

  29. Example of Momentum Conservation A 50 kg boy on roller skates moving with a speed of 5 m/s runs into a 40 kg girl also on skates. After the collision they cling together. What is their speed? G mb = 50 kg vb = 5 m/s mg = 40 kg vg = 0 m/s U

  30. Example of Momentum Conservation A 50 kg boy on roller skates moving with a speed of 5 m/s runs into a 40 kg girl also on skates. After the collision they cling together. What is their speed? G mb = 50 kg vb = 5 m/s mg = 40 kg vg = 0 m/s U vf = ? m/s

  31. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after

  32. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after mb vb + mg vb = mb vf + mg vf

  33. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after mb vb + mg vb = mb vf + mg vf vf (mb + mg) = mb vb + mg vb

  34. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after mb vb + mg vb = mb vf + mg vf vf (mb + mg) = mb vb + mg vb vf = mb vb + mgvg (m/s) (mb + mg)

  35. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after mb vb + mg vb = mb vf + mg vf vf (mb + mg) = mb vb + mg vb vf = mb vb + mgvg (m/s) (mb + mg) C , A vf = 50 x 5 + 40 x 0 50 + 40

  36. Example of Conservation of Momentum R Sum of Mom before = Sum of Mom after mb vb + mg vb = mb vf + mg vf vf (mb + mg) = mb vb + mg vb vf = mb vb + mgvg (m/s) (mb + mg) C , A vf = 50 x 5 + 40 x 0 = + 2.78 (m/s) 50 + 40

  37. Work Work is the product of the net Force times the distance moved in the direction of the net force. (Work) W = F d Work has units of Joules

  38. Work - Vertical Direction When an object is moved vertically, then Work = Weight height Work = m g h If work has a negative sign (-) it is being lost, if (+) it is being added to the system. In General ... Energy is the capacity to do work

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