SM_PDF_chapter8 - Momentum and Collisions CHAPTER OUTLINE...

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199 Momentum and Collisions CHAPTER OUTLINE 8.1 Linear Momentum and Its Conservation 8.2 Impulse and Momentum 8.3 Collisions 8.4 Two-Dimensional Collisions 8.5 The Center of Mass 8.6 Motion of a System of Particles 8.7 Context Connection Rocket Propulsion ANSWERS TO QUESTIONS Q8.1 No. Impulse, F t , depends on the force and the time for which it is applied. Q8.2 The momentum doubles since it is proportional to the speed. The kinetic energy quadruples, since it is proportional to the speed- squared. Q8.3 The momenta of two particles will only be the same if the masses of the particles of the same. Q8.4 (a) It does not carry force, for if it did, it could accelerate itself. (b) It cannot deliver more kinetic energy than it possesses. This would violate the law of energy conservation. (c) It can deliver more momentum in a collision than it possesses in its flight, by bouncing from the object it strikes. Q8.5 The superhero has finite mass. When he throws the piano, he must recoil in the opposite direction. To hover in midair, he must continuously fly by giving downward momentum to air, rocket exhaust or something that will disturb things below. Q8.6 No. Only in a precise head-on collision with momenta with equal magnitudes and opposite directions can both objects wind up at rest. Yes. Assume that ball 2, originally at rest, is struck squarely by an equal-mass ball 1. Then ball 2 will take off with the velocity of ball 1, leaving ball 1 at rest. Q8.7 Interestingly, mutual gravitation brings the ball and the Earth together. As the ball moves downward, the Earth moves upward, although with an acceleration 10 25 times smaller than that of the ball. The two objects meet, rebound, and separate. Momentum of the ball-Earth system is conserved. Q8.8 (a) Linear momentum is conserved since there are no external forces acting on the system. (b) Kinetic energy is not conserved because the chemical potential energy initially in the explosive is converted into kinetic energy of the pieces of the bomb.
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200 Momentum and Collisions Q8.9 Momentum conservation is not violated if we choose as our system the planet along with you. When you receive an impulse forward, the Earth receives the same size impulse backwards. The resulting acceleration of the Earth due to this impulse is significantly smaller than your acceleration forward, but the planet’s backward momentum is equal in magnitude to your forward momentum. Q8.10 Suppose car and truck move along the same line. If one vehicle overtakes the other, the faster- moving one loses more energy than the slower one gains. In a head-on collision, if the speed of the truck is less than m m m m T c T c + + 3 3 times the speed of the car, the car will lose more energy. Q8.11 The rifle has a much lower speed than the bullet and much less kinetic energy. The butt distributes the recoil force over an area much larger than that of the bullet.
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