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Unformatted text preview: CHAPTER 7 IMPULSE AND MOMENTUM ANSWERS TO FOCUS ON CONCEPTS QUESTIONS _____________________________________________________________________________________________ 1. (b) Kinetic energy, 2 1 2 mv , is a scalar quantity and is the same for both cars. Momentum, , m v is a vector quantity that has a magnitude and a direction. The two cars have different directions, so they have different momenta. 2. (d) Momentum is a vector quantity that has a magnitude and a direction. The magnitudes ( m v ) and directions (due north) are the same for both runners. 3. The magnitude of the total momentum is 47 700 kg m/s × . 4. (d) According to the impulse-momentum theorem, the impulse is equal to the final momentum minus the initial momentum. Therefore, the impulses are the same in both cases, since the final momenta are the same and the initial momenta are the same. The impulse is also the product of the net average force and the time of impact. Since the impulses are equal and the time of impact is larger for the air mattress than for the ground, the air mattress exerts a smaller net average force on the high jumper. 5. The impulse is 324 kg m/s + × . 6. (c) According to the impulse-momentum theorem, the impulse is equal to the change in the particle’s momentum. The magnitude of the momentum change is the same in regions A and C; therefore, in these regions the particle experiences impulses of the same magnitude. The momentum in region B is constant. Therefore, the change in momentum is zero, and so is the impulse. 7. (b) According to the impulse-momentum theorem, the net average force is equal to the change in the particle’s momentum divided by the time interval. This ratio is greatest in region C. The ratio is equal to zero in region B, since the change in the particle’s momentum is zero there. 8. Magnitude of net average force in Region A = 1.0 N, Magnitude of net average force in Region C = 4.0 N 9. (d) Since there are no external forces acting on the rocket, momentum is conserved before, during, and after the separation. This means that the momentum of the rocket before the separation (+150 000 kg ⋅ m/s) is equal to the sum of the momenta of the two stages after the separation [+250 000 kg ⋅ m/s + (- 100 000 kg ⋅ m/s) = +150 000 kg ⋅ m/s]. 86 IMPULSE AND MOMENTUM 10. (a) The net external force acting on the ball/earth system is zero. The gravitational forces that the ball and earth exert on each other are internal forces, or forces that the objects within the system exert on each other. The space probe is also an isolated system, since there are no external forces acting on it. 11. (c) The net external force that acts on the objects is zero, so the total linear momentum is conserved. Therefore, the total momentum before the collision (+12 kg ⋅ m/s - 2 kg ⋅ m/s = +10 kg ⋅ m/s) equals the total momentum after the collision (- 4 kg ⋅ m/s +14 kg ⋅ m/s = +10 kg ⋅ m/s)....
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