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Unformatted text preview: 9 CHAPTER OUTLINE 9.1 Linear Momentum and Its Conservation 9.2 Impulse and Momentum 9.3 Collisions in One Dimension 9.4 Two-Dimensional Collisions 9.5 The Center of Mass 9.6 Motion of a System of Particles 9.7 Rocket Propulsion Linear Momentum and Collisions ANSWERS TO QUESTIONS Q9.1 No. Impulse, F t , depends on the force and the time for which it is applied. Q9.2 The momentum doubles since it is proportional to the speed. The kinetic energy quadruples, since it is proportional to the speed-squared. Q9.3 The momenta of two particles will only be the same if the masses of the particles of the same. Q9.4 (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. Q9.5 Provided there is some form of potential energy in the system, the parts of an isolated system can move if the system is initially at rest. Consider two air-track gliders on a horizontal track. If you compress a spring between them and then tie them together with a string, it is possible for the system to start out at rest. If you then burn the string, the potential energy stored in the spring will be converted into kinetic energy of the gliders. Q9.6 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. Q9.7 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. Q9.8 (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. 251 252 Linear Momentum and Collisions Q9.9 Momentum conservation is not violated if we make our system include the Earth along with the clay. When the clay receives an impulse backwards, the Earth receives the same size impulse forwards. The resulting acceleration of the Earth due to this impulse is significantly smaller than the acceleration of the clay, but the planet absorbs all of the momentum that the clay loses. Q9.10 Momentum conservation is not violated if we choose as our system the planet along with you....
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