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Linear Momentum

Linear Momentum

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Linear Momentum

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  1. Linear Momentum Vectors again

  2. Review • Equations for Motion Along One Dimension

  3. Review • Motion Equations for Constant Acceleration • 1. • 2. • 3. • 4.

  4. Review • 3 Laws of Motion • If in Equilibrium • If not in equilibrium • Change in Motion is Due to Force • Force causes a change in acceleration

  5. Review • Work • Energy

  6. Review • Law of conservation of energy • Power • efficiency

  7. Collisions • If an 18 wheeler hits a car, what direction will the wreckage move? • What is the force between the 18 wheeler and the car?

  8. Forces

  9. Momentum • Newtons 2nd law • Linear momentum • SI • Newton defined it as quantity of motion

  10. Impulse • When an object collides with another, the forces on the object will momentarily spike before returning back to zero.

  11. Impulse

  12. Impulse • We now define impulse, J, as the change in momentum of a particle during a time interval • SI unit

  13. Example • A ball with a mass of 0.40 kg is thrown against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. (a) find the impulse of the net force on the ball during the collision with the wall. (b) If the ball is in contact with the wall for 0.010s, find the average horizontal force that the wall exerts on the ball during impact.

  14. Example

  15. Conservation of Momentum • If a particle A hits particle B

  16. Conservation of Momentum • If there are no external forces acting on the system

  17. Conservation of Momentum • Change in momentum over time is zero • The sum of momentums is constant

  18. Conservation of Momentum • If there are no external forces acting on a system, Total Momentum of a system conserved

  19. Vector Addition

  20. Example - Recoil • A marksman holds a rifle of mass 3.00 kg loosely such that it’ll recoil freely. He fires a bullet of mass 5.00g horizontally with velocity relative to the ground of 300 m/s. What is the recoil velocity of the rifle?

  21. Example - Recoil

  22. Example – 2D example • Two battling robots are on a frictionless surface. Robot A with mass 20 kg moves at 2.0 m/s parallel to the x axis. It collides with robot B, which has a mass of 12 kg. After the collision, robot A is moving at 1.0 m/s in a direction that makes an angle α=30o. What is the final velocity of robot B?

  23. Example

  24. Example

  25. Example

  26. Conservation of Momentum and Energy • Elastic Collisions – Collisions where the kinetic energies are conserved. When the particles are in contact, the energy is momentarily converted to elastic potential energy.

  27. Conservation of Momentum and Energy • Inelastic Collisions – collisions where total kinetic energy after the collision is less than before the collision. • Completely Inelastic Collisions- When the two particles stick together after a collision. • Collisions can be partly inellastic

  28. Completely Inelastic Collisions • Collisions where two objects will impact each other, but the objects stick together and move as one after the collision.

  29. Completely Inelastic Collisions • Momentum is still conserved • Find v in terms of v0

  30. Completely Inelastic Collisions • Assume Particle B is initially at rest

  31. Completely Inelastic Collisions • Kinetic Energy If B is at rest

  32. Examples – Young and Freedman 8.37 • At the intersection, a yellow subcompact car with mass travelling 950 kg east collides with a red pick up truck with mass 1900 kg travelling north. The two vehicles stick together and the wreckage travels 16.0 m/s 24o E of N. Calculate the speed of each of the vehicles. Assume frictionless.

  33. Young and Freedman 8.37

  34. Young and Freedman 8.37

  35. Problem – Ballistic Pendulum • The ballistic pendulum is an apparatus to measure the speed of a fast moving projectile, such as a bullet. A bullet of mass 12g with velocity 380 m/s is fired into a large wooden block of mass 6.0 kg suspended by a chord of 70cm. (a) Find the height the block rises (b) the initial kinetic energy of the bullet (c) The kinetic energy of the bullet and block.

  36. Problem – Ballistic Pendulum • Velocity after impact • Kinetic energy after impact

  37. Problem – Ballistic Pendulum • Kinetic energy after impact • Converted to potential at highest point

  38. Problem – Ballistic Pendulum

  39. Elastic Collisions • Momentum and Energy are conserved • Find v in terms of v0

  40. Elastic Collisions – One Dimension • If particle B is at rest

  41. Elastic Collisions – One Dimension • If particle B is at rest

  42. Elastic Collisions – One Dimension • If particle B is at rest • Substitute back

  43. Elastic Collisions – One Dimension • If particle B is at rest

  44. Elastic Collisions – One Dimension • If ma <<< mb • really small

  45. Elastic Collisions – One Dimension • If ma>>>mb • If ma=mb

  46. Example • In a game of billiards a player wishes to sink a target ball in the cornet pocket. If the angle to the corner pocket is 35o, at what angle is the cue ball deflected? (Assume frictionless)

  47. Example • Mass is the same

  48. Example

  49. Problem – Serway 9-36 • Two particles with masses m and 3m are moving towards each other along the x axis with the same initial speeds. Particle m is travelling towards the left and particle 3m is travelling towards the right. They undergo an elastic glancing collision such that particle m is moving downward after the collision at right angles from initial direction. (a) Find the final speeds of the two particles. (b) What is the angle θ at which particle 3m is scattered.

  50. Elastic Collisions and relative velocity – One Dimensional