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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 = D(m v) So Impulse =FNET D t

  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) So Impulse =FNET D t D(m v) = Change in Momentum

  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 = D(m v) = Change in Momentum

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

  12. CONSERVATION Conservation in Physics means that a quantity’s value does not change after certain physical processes. That is: the value of the quantityis thesamebefore and after the process. Which quantity’s are conserved?

  13. CONSERVED QUANTITIES Linear Momentum Angular Momentum

  14. CONSERVED QUANTITIES Linear Momentum Angular Momentum Total Energy Charge

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

  16. 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.

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

  18. Conserving Processes For 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.

  19. SOLVING QUANTATITIVE PROBLEMS GURU CA METHOD G Write Down the GIVENS ( Assign a symbol and unit for each value.)

  20. SOLVING QUANTATITIVE PROBLEMS GURU CA METHOD G Write Down the GIVENS ( Assign a symbol and unit for each value.) U Write down the UNKNOWN (Assign a symbol and unit)

  21. SOLVING QUANTATITIVE PROBLEMS GURU CA METHOD G Write Down the GIVENS ( Assign a symbol and unit for each value.) U Write down the UNKNOWN (Assign a symbol and unit) R Select a RELATIONSHIP (equation)

  22. SOLVING QUANTATITIVE PROBLEMS • U Determine if the UNITS desired can be directly determined from the givens. If not convert to the proper unit.

  23. 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

  24. 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

  25. 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

  26. 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

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

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

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

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

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

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

  33. 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

  34. 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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