Read Sections 10.4, 10.5, & 10.6

AP Physics-1 Work & Energy HW-2 Read Sections 10.4, 10.5, & 10.6 Conceptual Questions 1. (a) Is it possible for the kinetic energy of an object to be negative? (b) Is it possible for the gravitational potential energy of an object to be negative? Explain. 2. Taking a leap of faith, a bungee jumper steps off a platform and falls until the cord brings her to rest. Suppose you analyze this system, choosing y  0 either at the platform level or at the ground level. Will your answers agree or disagree on the following quantities: (a) The jumper’s initial and final potential energy; (b) the jumper’s change in potential energy? Explain. 3. A ball dropped to the floor rises to a height less than its original height. Discuss the energy conversions that take place in a system like this. 4. Is the change in gravitational potential energy of a stone that falls to the ground different from that of a stone that is thrown to the ground? Explain. 5. If the stretch of a spring is doubled, the force it exerts is also doubled. By what factor does the potential energy increase? 6. A mass is attached to the bottom of a vertical spring. This causes the spring to stretch and the mass to move downward. (a) Does the elastic potential energy of the spring increase or decrease? (b) Does the gravitational potential energy of the mass increase or decrease? 7. When a mass is placed on top of a vertical spring, the spring compresses and the mass moves downward. Analyze this system in terms of mechanical energy, indicating when each form is a maximum or minimum. 8. You and a friend both solve a problem involving a skier going down a slope. When comparing solutions, you notice that you have chosen different levels for y  0. Will your answers agree or disagree on the following quantities: (a) The skier’s potential energy; (b) the skier’s change in potential energy; (c) the skier’s kinetic energy? 9. If a spring is stretched so far that it is permanently deformed, its force is no longer conservative. Why? 10. A block slides on a frictionless, horizontal surface with a speed v until it encounters an ideal spring. The block compresses the spring a certain distance, d. When the spring expands again, what is the speed it gives to the block? 11. When an object is thrown upward to a person on a roof, at what point is the object’s (a) kinetic energy a maximum; (b) potential energy a maximum; (c) kinetic energy a minimum; and (d) potential energy a minimum? 12. You throw a ball upward and let it fall to the ground. Your friend drops an identical ball straight down to the ground from the same height. (a) Compare the change in gravitational potential energy for the two balls. (b) Compare the change in kinetic energies. Problems Conservative and Nonconservative Forces 1. • Calculate the work done by gravity as a 2.6-kg object is moved from point A to point B in Figure 1 along paths 1, 2, and 3.

Figure 1 Figure 2 2. • Calculate the work done by friction as a 2.6-kg box is slid along a floor from point A to point B in Figure 2 along paths 1, 2, and 3. Assume that the coefficient of kinetic friction between the box and the floor is 0.23. 3. • A 4.1-kg block is attached to a spring with a force constant of 550 N/m, as shown in Figure 3. (a) Find the work done by the spring on the block as the block moves from A to B along paths 1 and 2. (b) How do your results depend on the mass of the block?

Figure 3 4. •• In the system shown in Figure 3, suppose the block has a mass of 2.7 kg, the spring has a force constant of 480 N/m, and the coefficient of kinetic friction between the block and the floor is 0.16. (a) Find the work done on the block by the spring and by friction as the block is moved from point A to point B along path 2. (b) Find the work done on the block by the spring and by friction if the block is moved directly from point A to point B. Potential Energy and the Work Done by Conservative Forces 5. • As an Acapulco cliff diver drops to the water from a height of 40.0 m, his gravitational potential energy decreases by 25,000 J. How much does the diver weigh? 6. • Find the gravitational potential energy of an 80.0-kg person standing atop Mt. Everest, at an altitude of 8848 m. Use sea level as the location for y  0. 7. •• Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.50 cm, the spring potential energy is 0.0025 J. What compression is required for the spring potential energy to equal 0.0084 J? 8. •• If 30.0 J of work are required to stretch a spring from a 4.00-cm elongation to a 5.00-cm elongation, how much work is needed to stretch it from a 5.00-cm to a 6.00-cm elongation? 9. •• A 0.33-kg pendulum bob is attached to a string 1.2 m long. What is the change in the bob’s gravitational potential energy as it swings from point A to point B in Figure 4?

Figure 4 10. •• An 865-kg airplane starts at rest on an airport runway at sea level. (a) What is the change in mechanical energy of the airplane if it climbs to a cruising altitude of 2420 m and maintains a constant speed of 90.0 m/s? (b) What cruising speed would the plane need at this altitude if its increase in kinetic energy is to equal its increase in potential energy?

Answers

1. W1 = 51 J W2 = 51 J W3 = 51 J

2. W1 = 65 J W2 = 29 J W3 = 41 J

3. W1 = 0.11 J W2 = 0.11 J (b) The results have no dependence on the mass of the block.

4. (a) Wsp = 0.096 J Wf = 0.25 J (b) Wsp = 0.096 J Wf = 0.085 J 5. Weight = 625 N 6. PEg = 6.94 MJ 7. x = 0.92 cm

8. W = 36.7 J 9. PEg = 0.70 J 10. (a) ETOT = 24.0 MJ (b) v = 218 m/s