Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 58 | Concept Questions In a performance test two cars take the same time to accelerate from rest up to the same speed. Car A has a mass of 1400 kg, and car B has a mass of 1900 kg. During the test, which car (a) has the greater change in momentum, (b) experiences the greater impulse, and (c) is acted upon by the greater net average force? In each case, give your reasoning.
Problem Each car takes 9.0 s to accelerate from rest to 27 m/s. Find the net average force that acts on each car during the test. Verify that your answers are consistent with your answers to the Concept Questions.

| 59 | Concept Questions As the drawing illustrates, two disks with masses m1 and m2 are moving horizontally to the right at a speed v0. They are on an air-hockey table, which supports them with an essentially frictionless cushion of air. They move as a unit, with a compressed spring between them, which has a negligible mass. (a) When the spring is released and allowed to push outward, what are the directions of the forces that act on disk 1 and disk 2? (b) After the spring is released, is the speed of each disk larger than, smaller than, or the same as the speed v0 ? Explain.
Problem Consider the situation where disk 1 comes to a momentary halt shortly after the spring is released. Assuming that , , and , find the speed of disk 2 at that moment. Verify that your answer is consistent with your answers to the Concept Questions.

| 60 | Concept Questions A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon throws a rock. Does the momentum of the wagon increase, decrease, or remain the same (a) when the rock is thrown directly forward and (b) when the rock is thrown directly backward? (c) In which case does the wagon have the greater speed after the rock is thrown?
Problem The total mass of the wagon, rider, and rock is 95.0 kg. The mass of the rock is 0.300 kg. Initially the wagon is rolling forward at a speed of 0.500 m/s. Then the rock is thrown with a speed of 16.0 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown directly forward in one case and directly backward in another. Check to see that your answers are consistent with your answers to the Concept Questions.

| 61 | Concept Questions One object is at rest, and another is moving. Furthermore, one object is more massive than the other. The two collide in a one-dimensional completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. (a) Consider the final momentum of the two-object system after the collision. Is it greater when the large-mass object is moving initially or when the small-mass object is moving initially? (b) Is the final speed after the collision greater when the large-mass or the smallmass object is moving initially?
Problem The speed of the object that is moving initially is 25 m/s. The masses of the two objects are 3.0 and 8.0 kg. Determine the final speed of the two-object system after the collision for the case when the large-mass object is moving initially and the case when the small-mass object is moving initially. Be sure that your answers are consistent with your answers to the Concept Questions.

| 62 | Concept Questions Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. (a) Is it possible that the two-object system has a final total momentum of zero after the collision? (b) Roughly, what is the direction of the final total momentum of the two-object system after the collision?
Problem Object A has a mass of and an initial velocity of , due east. Object B, however, has a mass of and an initial velocity of , due north. Find the magnitude and direction of the total momentum of the two-object system after the collision. Make sure that your answers are consistent with your answers to the Concept Questions.

| 63 | Concept Questions (a) John has a larger mass than Barbara has. He is standing on the x axis at , while she is standing on the x axis at . Is their centerof-mass point closer to the 9.0-m point or the 2.0-m point? (b) They switch positions. Is their center-of-mass point now closer to the 9.0-m point or the 2.0-m point? (c) In which direction, toward or away from the origin, does their center of mass move as a result of the switch?
Problem John’s mass is 86 kg, and Barbara’s is 55 kg. How far and in which direction does their center of mass move as a result of the switch? Verify that your answer is consistent with your answers to the Concept Questions.

| 64 | Concept Questions A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. (a) During the downward motion of the ball, are any of the following conserved: its momentum, its kinetic energy, its total mechanical energy? (b) During the collision with the block, are any of the following conserved: the horizontal component of the total momentum of the ball/block system, the total kinetic energy of the system? Provide reasons for your choices.
Problem The masses of the ball and block are, respectively, 1.60 kg and 2.40 kg, and the length of the wire is 1.20 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

| 65 | Concept Questions Part a of the drawing shows a bullet approaching two blocks resting on a horizontal frictionless surface. Air resistance is negligible. The bullet passes completely through the first block (an inelastic collision) and embeds itself in the second one, as indicated in part b. Note that both blocks are moving after the collision with the bullet. (a) Can the conservation of linear momentum be applied to this three-object system, even though the second collision occurs a bit later than the first one? Justify your answer. Neglect any mass removed from the first block by the bullet. (b) Is the total kinetic energy of this three-body system conserved? If not, would the total kinetic energy after the collisions be greater than or smaller than that before the collisions? Justify your answer.
Problem A 4.00-g bullet is moving horizontally with a velocity of + 355 m/s, where the + sign indicates that it is moving to the right. The mass of the first block is 1150 g, and its velocity is + 0.550 m/s after the bullet passes through it. The mass of the second block is 1530 g. (a) What is the velocity of the second block after the bullet imbeds itself? (b) Find the ratio of the total kinetic energy after the collision to that before the collision. Be sure your answer is consistent with that in part (b) of the Concept Questions.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.