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Momentum

Momentum. Momentum and Collisions. This chapter is concerned with inertia and motion. Momentum helps us understand collisions. Momentum. Inertia in motion mass => quantity of matter in an object inertia => an object's resistance to change in motion. Momentum Defined.

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Momentum

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  1. Momentum

  2. Momentum and Collisions • This chapter is concerned with inertia and motion. • Momentum helps us understand collisions.

  3. Momentum • Inertia in motion • mass => quantity of matter in an object • inertia => an object's resistance to change in motion

  4. Momentum Defined The quantity of motion, momentum, as being directly proportional to the object's mass and velocity. Momentum is a vector quantity……. ……..because it is a scalar (mass) of the vector velocity.

  5. p = Mv

  6. Momentum • Momentum = mass X velocity

  7. Momentum Defined  = mv where  is momentum with units kgm/s m is the mass with units kg v is the velocity with units m/s

  8. Momentum Defined Very Fast objects have Greeeeat momentum Very Massive Objects have Greeeat momentum

  9. Momentum • If Direction Not Important……….. • …….Momentum = mass x speed • Therefore……..p = ms

  10. A large truck has more momentum than a car moving at the same speed because it has a greater mass. • Which is more difficult to slow down? The car or the large truck?

  11. Large Momentum Examples: • Huge ship moving at a small velocity • High velocity bullet P = mv P = mv

  12. Impulse • In order to change the momentum of an object you must apply a force over some time interval. • Impulse = Force ´ time interval •  p= F t

  13. Impulse • Newton’s Second Law can read SF = ma = m(Dv/Dt) = (Dmv)/(Dt) = (Dp/ Dt) Rearranging, Impulse = Dp = FDt

  14. Impulse • When force is limited ... • increase Dt (Follow through!) • make it bounce (Pelton wheel)

  15. Impulse and Momentum • Impulse = Change in Momentum • = Final (mv) - Initial (mv) • F t = mDv

  16. Make it Bounce p1 p2 = -p1 Dp = p2 - p1 = -p1 - p1 = -2p1

  17. Case 1: Increasing Momentum • Apply a force for a long time. • Examples: • Follow through on a golf swing. • Pushing a car. FDt

  18. Case 2: Decreasing Momentum • Apply a force for a long time. • Examples: • Air bags in cars. • Catching an egg. • Boxing, Figure 5.6 • Soft collisions, Figure 5.3. FDt

  19. Case 3: Decreasing Momentum • Apply a force for a short time. • Examples: • Boxing • Karate FDt

  20. Minimize the Force • To minimize force … • Increase Dt • catching a ball • Bungee jumping

  21. Conservation of Momentum • If SF = 0, then impulse = Dp = zero, or Momentum is conserved

  22. Conservation of Momentum • This means that the momentum doesn’t change. • Recall that F t = D(mv) • In this equation, F is the "external force". • Internal forces cannot cause a change in momentum.

  23. Examples • Conservation of Momentum: If there are no external forces, the total momentum for a system remains unchanged. • Example 1: a person sitting inside a car pushing against the dashboard • Example 2: a bullet fired from a rifle • Example 3: a rocket is space

  24. Conservation of Momentum

  25. Conservation of Momentum

  26. Conservation of Momentum • In any "closed system" the total momentum does not change.

  27. Conservation of Momentum • ……..(Total momentum)before event = (Total momentum) after event (mbvb + mrvr) before = (mbvb + mrvr) after

  28. Demonstrations • Rocket balloon • Cannon • Rocket Scooter

  29. When can Momentum be Conserved? • Internal forces cannot cause a change in momentum of the system. • For conservation of momentum, the external forces must be zero.

  30. Momentum and Collisions • Elastic Collisions • objects rebound • e.g. superball • Inelastic Collisions • object stick together an usually become distorted and generate heat • e.g. clay ball

  31. COLLISIONS • Collisions involve forces internal to colliding bodies. • Inelastic collisions - conserve momentum • Totally inelastic collisions - conserve momentum and objects stick together • Elastic collisions - conserve energy and momentum

  32. M M M M Inelastic Collisions v = 10 v = 0 Before Collision p = Mv v’ = 5 After Collision p = 2Mv’ Mv = 2Mv’ v’ = ½ v

  33. Elastic Collisions Conserve Energy and Momentum Before Collision Equal masses Case 1: Case 2: M > M Case 3: M < M

  34. Momentum = Mass x Velocity p = mv

  35. v p = mv

  36. Elastic and inelastic collision

  37. V1 V2 M M Before Collision V2’ V1’ M M After Collision

  38. Types of Collisions 1. Elastic 2. Inelastic collisions 3. Completely Inelastic collisions

  39. Elastic Collisions Momentum…. is conserved in every collision Kinetic Energy…..is conserved……. …..No sound or heat is produced

  40. Elastic Collisions Examples….. Subatomic particles repelling magnets a “perfect”super ball

  41. Elastic Collisions M1v1o + m2 v2o = m1 v1f +m2v2f

  42. Inelastic Collisions Momentum…... is conserved Kinetic Energy……. is not conserved lost in form of heat or sound Contains almost all types of collisions

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