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Chapter 6: Momentum and Collisions

Chapter 6: Momentum and Collisions. Objectives. Understand the concept of momentum. Use the impulse-momentum theorem to solve problems. Understand how time and force are related in collisions. Momentum. momentum : inertia in motion; the product of mass and velocity. p = m · v.

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Chapter 6: Momentum and Collisions

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  1. Chapter 6: Momentum and Collisions

  2. Objectives • Understand the concept of momentum. • Use the impulse-momentum theorem to solve problems. • Understand how time and force are related in collisions.

  3. Momentum momentum: inertia in motion; the product of mass and velocity p = m · v How much momentum does a 2750 kg Hummer H2 moving at 31 m/s possess? Note: momentum is a vector; units are kg·m/s

  4. Impulse Changes Momentum Newton actually wrote his second law in this form: SF · Dt = m · Dv The quantity SF·Dtis called impulse. The quantity m·Dvrepresents a change in momentum. Thus, an impulse causes a change in momentum SF SF·Dt = m·Dv = Dp “impulse-momentum theorem”

  5. Highway Safety and Impulse Water-filled highway barricades increase the time it takes to stop a car. Why is this safer? They reduce the force during impact! SF = (m · Dv) / Dt Seatbelts and airbags also increase the stopping time and reduce the force of impact.

  6. Impulse Problem A car traveling at 21 m/s hits a concrete wall. If the 72 kg passenger is not wearing a seatbelt, he hits the dashboard and stops in 0.13 s. • What is the Dp? • How much impulse is applied to the passenger? • How much force does the dashboard apply to the passenger? What is the force applied to the passenger if he is wearing a seatbelt takes 0.62 s to stop?

  7. Impulse Problem The face of a golf club applies an average force of 5300 N to a 49 gram golf ball. The ball leaves the clubface with a speed of 44 m/s. How much time is the ball in contact with the clubface? SF·Dt = m·Dv SF

  8. Bouncing Which collision involves more force: a ball bouncing off a wall or a ball sticking to a wall? Why? The ball bouncing because there is a greater Dv. SF · Dt = m · Dv so SF ~ Dv Pelton wheel

  9. Objectives • Understand the concept of conservation of momentum. • Understand why momentum is conserved in an interaction. • Be able to solve problems involving collisions.

  10. Conservation of Momentum conservation of momentum: in any interaction (such as a collision) the total combined momentum of the objects remains unchanged (as long as no external forces are present). system: all of the objects involved in an interaction

  11. system Conservation of Momentum ma·vai + mb·vbi = Spi mb ma vai vbi -Dp = -SF · Dt -SF +SF Dp = +SF · Dt Dt DpTOTAL = ( -SF·Dt ) + ( +SF·Dt ) = 0 ma·vaf + mb·vbf = Spf mb ma S pi=S pf vaf vbf Law of Conservation of Momentum: ma·vai + mb·vbi = ma·vaf + mb·vbf

  12. Slingshot Manuever The spacecraft is pulled toward Jupiter by gravity, but as Jupiter moves along its orbit, the spacecraft just misses colliding with the planet and speeds up. The spacecraft substantially increased its momentum (as speed) and Jupiter lost the same amount of momentum, but because Jupiter is so massive, its overall speed remained virtually unchanged. Jupiter S pi=S pf

  13. Conservation of Momentum Problem A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.6 m/s. How fast does the target ball (“pallino”) move? Assume all motion is in one dimension. ma·vai + mb·vbi = ma·vaf + mb·vbf

  14. Objectives • Understand the difference between elastic and inelastic collisions. • Solve problems involving conservation of momentum during an inelastic collision.

  15. Collisions • elastic: objects collide and rebound, maintaining shape • both KE and p are conserved (DEMO—Newton spheres) • perfectly inelastic: objects collide, deform, and combine into one mass • KE is not conserved (becomes sound, heat, etc.) • real collisions are usually somewhere in between

  16. Types of Collisions elastic ma·vai + mb·vbi = ma·vaf + mb·vbf perfectly inelastic ma·vai + mb·vbi = (ma+ mb) ·vf

  17. Conservation of Momentum Problem Victor, who has a mass of 85 kg, is trying to make a “get-away” in his 23-kg canoe. As he is leaving the dock at 1.3 m/s, Dakota jumps into the canoe and sits down. If Dakota has a mass of 64 kg and she jumps at a speed of 2.7 m/s, what is the final speed of the the canoe and its passengers?

  18. Conservation of Momentum in Two-Dimensions Collisions in 2-D involve vectors. paf ma initial ma mb final Spi mb pbf

  19. Equal Mass Collision A cue ball (m = 0.16 kg) rolling at 4.0 m/s hits a stationary eight ball of the same mass. If the cue ball travels 25o above its original path and the eight ball travels 65o below the original path, what is the speed of each ball after the collision?

  20. Unequal Mass Collision A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.8 m/s and travels at a 15o angle above its original path. What is the speed of the target ball it travels at a 75o below the original path?

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