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Unformatted text preview: 9 Linear Momentum and Collisions 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 Deformable Systems 9.8 Rocket Propulsion ANSWERS TO QUESTIONS *Q9.1 (a) No. Impulse, r F ∆ t , depends on the force and the time for which it is applied. (b) No. Work depends on the force and on the distance over which it acts. *Q9.2 The momentum magnitude is proportional to the speed and the kinetic energy is proportional to the speed squared. (i) The speed of the constant-mass object becomes 4 times larger and the kinetic energy 16 times larger. Answer (a). (ii) The speed and the momentum become two times larger. Answer (d). *Q9.3 (i) answer (c). For example, if one particle has 5 times larger mass, it will have 5 times smaller speed and 5 times smaller kinetic energy. (ii) answer (d). Momentum is a vector. *Q9.4 (i) Equal net work inputs imply equal kinetic energies. Answer (c). (ii) Imagine one particle has four times more mass. For equal kinetic energy it must have half the speed. Then this more massive particle has 4(1 / 2) = 2 times more momentum. Answer (a). Q9.5 (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 ﬂ ight, by bouncing from the object it strikes. *Q9.6 Mutual gravitation brings the ball and the Earth together. As the ball moves downward, the Earth moves upward, although with an acceleration on the order of 10 25 times smaller than that of the ball. The two objects meet, rebound, and separate. Momentum of the ball-Earth system is conserved. Answer (d). Q9.7 (a) Linear momentum is conserved since there are no external forces acting on the system. The fragments go off in different directions and their vector momenta add to zero. (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. 209 13794_09_ch09_p209-244 copy.indd209 209 13794_09_ch09_p209-244 copy.indd209 209 1/8/07 5:47:49 PM 1/8/07 5:47:49 PM Q9.8 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 much smaller than your acceleration forward, but the planet’s backward momentum is equal in magnitude to your forward momentum. *Q9.9 (i) During the short time the collision lasts, the total system momentum is constant. Whatever momentum one loses the other gains. Answer (c)....
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