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Collisions: Momentum and Impulse

Collisions: Momentum and Impulse. SC.CE.05.01. The product of the mass of an object and its velocity Momentum = “ p ” p= m v If mass is constant, then a change of momentum equals mass times change in velocity: Δ p= m Δ v A vector quantity Vector means…. Momentum:. Impulse:.

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Collisions: Momentum and Impulse

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  1. Collisions: Momentum and Impulse SC.CE.05.01

  2. The product of the mass of an object and its velocity Momentum = “p” p=mv If mass is constant, then a change of momentum equals mass times change in velocity: Δp=mΔv A vector quantity Vector means… Momentum:

  3. Impulse: • The average force multiplied by its time interval of action • Impulse = FΔt • A vector quantity • Vector means…

  4. Simply stated: • Impulse = change in momentum =Δp

  5. Impulse/momentum principle: • The impulse acting on an object produces a change in momentum of the object that is equal both in magnitude and direction to the impulse

  6. For example: m=7kg v=2m/s p=14kg ×m/s m=0.07kg v=200m/s p=14 kg × m/s

  7. Conservation of Momentum: • When the net external force acting on a system is zero, the total momentum of the system is conserved • In other words: the momentum before a collision will equal the momentum after a collision • When internal forces are equal (but opposite), momentum is conserved

  8. Example: • A 100 kg fullback moving straight downfield with a velocity of 5 m/s collides head on with a 75 kg defensive back moving in the opposite direction with a velocity of -4m/s. The defensive back hangs on to the fullback, and the two players move together after the collision. • a. What is the initial momentum of each player? • b. What is the total momentum of the system? • c. What is the velocity of the two players immediately after the collision?

  9. Fullback: m = 100 kg v = 5 m/s p = ? p = mv p = Defensive back: m = 75 kg v = -4 m/s p = ? p = mv p = Example (cont’d) a: What is the initial momentum of each player?

  10. b. What is the total momentum of the system? • p total = p fullback + p defensive back • p total = 500 kg x m/s + -300 kg x m/s • p total = 200 kg x m/s

  11. v=? m= 100 kg + 75 kg =175 kg p=mv So: v=p/m v= 200 kg x m/s 175 kg c. What is the velocity of the two players immediately after the collision?

  12. Types of Collisions: Perfectly Inelastic to Perfectly Elastic Extend your knowledge of momentum and energy conservation!

  13. Perfectly Inelastic Collisions • A collision in which the objects stick together after colliding • No bounce • If p is known before collision for both objects, we simply add them together to get final p • A lot of the original kinetic energy is transformed • Example: railroad car coupling, two balls of clay, a football tackle

  14. Partially Inelastic • Some kinetic energy is transformed

  15. Elastic • No kinetic energy is transformed • Atoms collide without “spending” energy

  16. When pool balls collide: • Most collisions are elastic: both momentum and kinetic energy are conserved • Momentum is transferred from the cue ball to the target ball • We can determine the velocity of both balls after collision • It gets tricky when multiple pool balls are involved, but I know you can do it!

  17. Collisions at an Angle Oh geez, here we go…

  18. An Inelastic Two-Dimensional Collision: • Remember that momentum is a vector quantity? • Now our football players from Monday are running perpendicular to one another 583 kg x m/s p2=300kg x m/s 31° p1=500kg x m/s

  19. Elastic Two-Dimensional Collisions • Initial kinetic energy = 1/2mv2 must also equal the sum of the kinetic energies

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