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Chapter 9 Momentum Topics: • Impulse • Momentum • The impulse-momentum theorem • Conservation of momentum • Inelastic collisions Sample question: Male rams butt heads at high speeds in a ritual to assert their dominance. How can the force of this collision be minimized so as to avoid damage to their brains? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-1 Reading Quiz 1. Impulse is A. a force that is applied at a random time. B. a force that is applied very suddenly. C. the area under the force curve in a force-versus-time graph. D. the interval of time that a force lasts. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-2 Answer 1. Impulse is C. the area under the force curve in a force-versus-time graph. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-3 Reading Quiz 2. The total momentum of a system is conserved A. always. B. if no external forces act on the system. C. if no internal forces act on the system. D. never; momentum is only approximately conserved. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-4 Answer 2. The total momentum of a system is conserved B. if no external forces act on the system. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-5 Reading Quiz 3. In an inelastic collision, A. impulse is conserved. B. momentum is conserved. C. force is conserved. D. energy is conserved. E. elasticity is conserved. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-6 Answer 3. In an inelastic collision, B. momentum is conserved. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-7 Impulse The force of the foot on the ball is an impulsive force. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-8 Graphical Interpretation of Impulse J = Impulse = area under the force curve Favg t Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-9 Momentum Momentum is the product of an object’s mass and its velocity: p = mv Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-10 The Impulse-Momentum Theorem Impulse causes a change in momentum: J =pf - pi = ∆p Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-11 Example A 0.5 kg hockey puck slides to the right at 10 m/s. It is hit with a hockey stick that exerts the force shown. What is its approximate final speed? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-12 Checking Understanding Two 1-kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? A. Ball 1 B. Ball 2 C. Both balls have the same final speed Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-13 Answer Two 1-kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? C. Both balls have the same final speed Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-14 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-15 Example A car traveling at 20 m/s crashes into a bridge abutment. Estimate the force on the driver if the driver is stopped by A. a 20-m-long row of water-filled barrels B. the crumple zone of her car (~1 m). Assume a constant acceleration. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-16 Example A 500 kg rocket sled is coasting at 20 m/s. It then turns on its rocket engines for 5.0 s, with a thrust of 1000 N. What is its final speed? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-17 The Law of Conservation of Momentum In terms of the initial and final total momenta: Pf = P i In terms of components: Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-18 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-19 Example A curling stone, with a mass of 20.0 kg, slides across the ice at 1.50 m/s. It collides head on with a stationary 0.160-kg hockey puck. After the collision, the puck’s speed is 2.50 m/s. What is the stone’s final velocity? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-20 Inelastic Collisions For now, we’ll consider perfectly inelastic collisions: A perfectly elastic collision results whenever the two objects move off at a common final velocity. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-21 Example Jack stands at rest on a skateboard. The mass of Jack and the skateboard together is 75 kg. Ryan throws a 3.0 kg ball horizontally to the right at 4.0 m/s to Jack, who catches it. What is the final speed of Jack and the skateboard? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-22 Example A 10 g bullet is fired into a 1.0 kg wood block, where it lodges. Subsequently, the block slides 4.0 m across a floor (µk = 0.20 for wood on wood). What was the bullet’s speed? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-23