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 problemsolving technique.

| 112 | Concept Questions Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The woman pushes on the man with a certain force that is parallel to the ground. (a) Must the man accelerate under the action of this force? If so, what three factors determine the magnitude and direction of his acceleration? (b) Is there a corresponding force exerted on the woman? If so, where does it originate? Is this force related to the magnitude and direction of the force the woman exerts on the man? If so, how?
Problem The mass of the man is 82 kg and that of the woman is 48 kg. The woman pushes on the man with a force of 45 N due east. Determine the acceleration (magnitude and direction) of (a) the man and (b) the woman.

| 113 | Concept Questions A person is attempting to push a refrigerator across a room. He exerts a horizontal force on the refrigerator, but it does not move. (a) What other horizontal force must be acting on the refrigerator? (b) How are the magnitude and direction of this force related to the force that the person exerts? (c) Suppose that the person applies the force such that it is the largest possible force before the refrigerator begins to move. What factors determine the magnitude of this force?
Problem Consult Multiple-Concept Example 9 to explore a model for solving this problem. A person pushes on a 57-kg refrigerator with a horizontal force of −267 N; the minus sign indicates that the force is directed along the −x direction. The coefficient of static friction is 0.65. (a) If the refrigerator does not move, what is the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? (b) What is the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move?

| 114 | Concept Questions A large rock and a small pebble are held at the same height above the ground. (a) Is the gravitational force exerted on the rock greater than, less than, or equal to that exerted on the pebble? Justify your answer. (b) When the rock and the pebble are released, is the downward acceleration of the rock greater than, less than, or equal to that of the pebble? Why?
Problem A 5.0-kg rock and a pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the acceleration of each object when released. Verify that your answers are consistent with your answers to the Concept Questions.

| 115 | Concept Questions The earth exerts a gravitational force on a falling raindrop, pulling it down. Does the raindrop exert a gravitational force on the earth, pulling it up? If so, is this force greater than, less than, or equal to the force that the earth exerts on the raindrop? Provide a reason for your answer.
Problem A raindrop has a mass of , and is falling near the surface of the earth. Calculate the magnitude of the gravitational force exerted (a) on the raindrop by the earth and (b) on the earth by the raindrop.

| 116 | Concept Questions Two horizontal forces, and , are acting on a box, but only is shown (see the drawing). can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. What is the direction of and how does its magnitude compare to the magnitude of when the acceleration of the box is (a) positive, (b) negative, and (c) zero?
Problem Suppose that = +9.0 N and the mass of the box is 3.0 kg. Find the magnitude and direction of when the acceleration of the box is (a) +5.0 m/s2, (b) −5.0 m/s2, and (c) 0 m/s2. Be sure that your answers are consistent with your answers to the Concept Questions.

| 117 | Concept Questions A car is driving up a hill. (a) Is the magnitude of the normal force exerted on the car equal to the magnitude of its weight? Why or why not? (b) If the car drives up a steeper hill, does the normal force increase, decrease, or remain the same? Justify your answer. (c) Does the magnitude of the normal force depend on whether the car is traveling up the hill or down the hill? Give your reasoning.
Problem A car is traveling up a hill that is inclined at an angle of above the horizontal. Determine the ratio of the magnitude of the normal force to the weight of the car when (a) and (b) . Check to see that your answers are consistent with your answers to the Concept Questions.

| 118 | Concept Questions Two blocks are sliding to the right across a horizontal surface, as the drawing shows. In Case A the masses of both blocks are 3.0 kg. In Case B the mass of block 1, the block behind, is 6.0 kg, and the mass of block 2 is 3.0 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force does act on block 2 in both cases and opposes the motion. (a) Identify the forces that contribute to the horizontal net force acting on block 1. (b) Identify the forces that contribute to the horizontal net force acting on block 2. (c) In which case, if either, do the blocks push against each other with greater forces? Explain. (d) Are the blocks accelerating or decelerating, and in which case, if either, is the magnitude of the acceleration greater?
Problem The magnitude of the kinetic frictional force acting on block 2 in the drawing is 5.8 N. For both Case A and Case B deterine (a) the magnitude of the forces with which the blocks push against each other and (b) the acceleration of the blocks. Check to see that your answers are consistent with your answers to the Concept Questions.

| 119 | Concept Questions A block is pressed against a vertical wall by a force , as the drawing shows. This force can either push the block upward at a constant velocity or allow it to slide downward at a constant velocity, the magnitude of the force being different in the two cases, while the directional angle is the same. Kinetic friction exists between the block and the wall. (a) Is the block in equilibrium in each case? Explain. (b) In each case what is the direction of the kinetic frictional force that acts on the block? Why? (c) In each case is the magnitude of the frictional force the same or different? Justify your answer. (d) In which case is the magnitude of the force greater? Provide a reason for your answer.
Problem The weight of the block is 39.0 N, and the coefficient of kinetic friction between the block and the wall is 0.250. The direction of the force is . Determine the magnitude of when the block slides up the wall and when it slides down the wall. Check to see that your answers are consistent with your answers to the Concept Questions.

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