Chapter 5: More Applications of Newton’s Laws
1. You press your physics textbook flat against a vertical wall with your hand, which applies a force perpendicular to the book. What is the direction of the friction force on the book due to the wall? (a) downward (b) upward (c) out from the wall (d) into the wall
Answer: (b). The friction force acts opposite to the weight of the book to keep the book in equilibrium. Because the weight is downward, the friction force must be upward.
2. A crate is located in the center of a flatbed truck. The truck accelerates to the east and the crate moves with it, not sliding at all. What is the direction of the friction force exerted by the truck on the crate? (a) It is to the west. (b) It is to the east. (c) No friction force exists because the crate is not sliding.
Answer: (b). The crate accelerates to the east. Because the only horizontal force acting on it is the force of static friction between its bottom surface and the truck bed, that force must also be directed to the east.
3. You are playing with your daughter in the snow. She sits on a sled and asks you to slide her across a flat, horizontal field. You have a choice of (a) pushing her from behind, by applying a force downward on her shoulders at 30° below the horizontal (Fig. 5.2a) or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal (Fig 5.2b). Which would require less force for a given acceleration of the daughter?
Figure 5.2 A father tries to slide his daughter on a sled over snow by (a) pushing downward on her shoulders or (b) pulling upward on a rope attached to the sled. Which is easier?
Answer: (b). When pulling with the rope, there is a component of your applied force that is upward, which reduces the normal force between the sled and the snow. In turn, the friction force between the sled and the snow is reduced, making the sled easier to move. If you push from behind, with a force with a downward component, the normal force is larger, the friction force is larger, and the sled is harder to move.
4. You are riding on a Ferris wheel (Fig. 5.10) that is rotating with constant speed. The car in which you are riding always maintains its correct upward orientation; it does not invert. (i) What is the direction of the normal force on you from the seat when you are at the top of the wheel? (a) upward (b) downward (c) impossible to determine. (ii) What is the direction of the net force on you when you are at the top of the wheel? (a) upward (b) downward (c) impossible to determine
(© Tom Carroll/Index Stock Imagery/PictureQuest)
Figure 5.10 A Ferris wheel located on Navy Pier in Chicago, Illinois.
Answer: (i), (a). The normal force is always perpendicular to the surface that applies the force. Because your car maintains its orientation at all points on the ride, the normal force is always upward. (ii), (b). Your centripetal acceleration is downward toward the center of the circle, so the net force on you must be downward.
5. Which of the following is impossible for a car moving in a circular path? Assume that the car is never at rest. (a) The car has tangential acceleration but no centripetal acceleration. (b) The car has centripetal acceleration but no tangential acceleration. (c) The car has both centripetal acceleration and tangential acceleration.
Answer: (a). If the car is moving in a circular path, it must have centripetal acceleration given by Equation 3.17:
6. A bead slides freely along a horizontal, curved wire at constant speed, as shown in Figure 5.16. (a) Draw the vectors representing the force exerted by the wire on the bead at points , , and . (b) Suppose the bead in Figure 5.16 speeds up with constant tangential acceleration as it moves toward the right. Draw the vectors representing the force on the bead at points , , and .
Figure 5.16 A bead slides along a curved wire.
Answer: (a) Because the speed is constant, the only direction the force can have is that of the centripetal acceleration. The force is larger at than at because the radius at is smaller. There is no force at because the wire is straight. (b) In addition to the forces in the centripetal direction in (a), there are now tangential forces to provide the tangential acceleration. The tangential force is the same at all three points because the tangential acceleration is constant.
Figure QQA.5.6
7. Consider a sky surfer falling through air, as in Figure 5.20, before reaching her terminal speed. As the speed of the sky surfer increases, the magnitude of her acceleration (a) remains constant, (b) decreases until it reaches a constant nonzero value, or (c) decreases until it reaches zero.
(Jump Run Productions/Image Bank)
Figure 5.20 A sky surfer takes advantage of the upward force of the air on her board.
Answer: (c). When the downward gravitational force and the upward force of air resistance have the same magnitude, she reaches terminal speed and her acceleration is zero.