Chapter 5EnergyQuick QuizzesAnswers to Even Numbered Conceptual QuestionsAnswers to Even Numbered ProblemsProblem SolutionsEnergy 143Chapter 5EnergyQuick Quizzes1. (c). The work done by the force is ( )cosW F x q= D, where q is the angle between the direction of the force and the direction of the displacement (positive x-direction). Thus, the work has its largest positive value in (c) where 0q = �, the work done in (a) is zero since 90q = �, the work done in (d) is negative since 90 270q�< < �, and the work done is most negative in (b) where 180q = �.2. (d). All three balls have the same speed the moment they hit the ground because all start with the same kinetic energy and undergo the same change in gravitational potential energy.3. (c). They both start from rest, so the initial kinetic energy is zero for each of them. They have the same mass and start from the same height, so they have the same initial potentialenergy. Since neither spends energy overcoming friction, all of their original potential energy will be converted into kinetic energy as they move downward. Thus, they will haveequal kinetic energies when they reach the ground.4. (c). The decrease in mechanical energy of the system is fkx. This has a smaller value on the tilted surface for two reasons: (1) the force of kinetic friction fk is smaller because the normal force is smaller, and (2) the displacement x is smaller because a component of thegravitational force is pulling on the book in the direction opposite to its velocity.144 CHAPTER 5Answers to Even Numbered Conceptual Questions 2. (a) The chicken does positive work on the ground. (b) No work is done. (c) The crane doespositive work on the bucket. (d) The force of gravity does negative work on the bucket. (e) The leg muscles do negative work on the individual. 4. (a) Kinetic energy is always positive. Mass and speed squared are both positive. (b) Gravitational potential energy can be negative when the object is lower than the chosen reference level. 6. (a) Kinetic energy is proportional to the speed squared. Doubling the speed makes the object’s kinetic energy four times larger. (b) If the total work done on an object in some process is zero, its speed must be the same at the final point as it was at the initial point. 8. The total energy of the bowling ball is conserved. Because the ball initially has gravitational potential energy mgh and no kinetic energy, it will again have zero kinetic energy when it returns to its original position. Air resistance and friction at the support will cause the ball to come back to a point slightly below its initial position. On the other hand, if anyone gives a forward push to the ball anywhere along its path, the demonstrator will have to duck.10. (a) The effects are the same except for such features as having to overcome air resistance outside. (b) The person must lift his body slightly with each step on the tilted treadmill. Thus, the effect is that of running uphill.12. Both the force of kinetic friction exerted on the sled by the snow and the resistance force exerted on the moving sled by the air will do negative work on the sled. Since the sled is maintaining constant velocity, some towing agent must do an equal amount of positive work, so the net work done on the sled is zero.14. The kinetic energy is converted to internal energy within the brake pads of the car, the roadway, and the tires.16. Work is actually performed bythe thigh bone (the femur) onthe hips as the torso movesupwards a distance h. The forceon the torso torsoFr isapproximately the same as thenormal force (since the legs arerelatively light and are notmoving much), and the workEnergy 145done by torsoFr minus the work done by gravity is equal to the change in kinetic energy of the torso.At full extension the torso would continue upwards, leaving the legs behind on the ground (!), except that the torso now does work on the legs, increasing their speed (and decreasing the torso speed) so that both move upwards together.Note: An alternative way to think about problems that involve internal motions of an objectis to note that the net work done on an object is equal to the net force times the displacement of the center of mass. Using this idea, the effect of throwing the arms upwards during the extension phase is accounted for by noting that the position of the center of mass is higher on the body with the arms extended, so that total displacement ofthe center of mass is greater.18. The normal force is always perpendicular to the surface and the motion is generally parallel to the surface. Thus, in most circumstances, the normal force is perpendicular to the displacement and does no work. The force of static friction does no work because thereis no displacement of the object relative to the surface in a static situation.20.