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POTENTIAL ENERGY AND ENERGY CONSERVATION ? As this diver enters the water, is the force of gravity doing positive or negative work on him? Is the water doing positive or negative work on him? When a diver jumps off a high board into a swimming pool, he hits the water moving pretty fast, with a lot of kinetic energy. Where does that energy come from? The answer we learned in Chapter 6 was that the gravitational force (his weight) does work on the diver as he falls. The diver's kinetic energy--energy associated with his motion-increases by an arnount equal to the work done. However, there is a very useful alternative way to think: about work and kinetic energy. This new approach is based on the concept of potential energy, which is energy associated with the position of a system rather than its motion. In this approach, there is gravitational potential energy even while the diver is standing on the high board. Energy is not added to the earth-diver system as the diver falls, but rather a storehouse of energy is transformed from one form (potential energy) to another (kinetic energy) as he falls. In this chapter we'll see how the work-energy theorem explains this transfonnation. If the diver bounces on the end of the board before he jwnps, the bent board stores a second kind of potential energy called elastic potential energy. We'll dis-cuss elastic potential energy of simple systems such as a stretched or compressed spring. (An important third kind of potential energy is associated with the posi-tions of electrically charged particles relative to each other. We'll encounter this potential energy in Chapter 23.) We will prove that in some cases the swn of a system's kinetic and potential energy, called the total mechanical energy of the system, is constant during the motion of the system. This will lead us to the general statement of the law of con-servation of energy, one of the most fundamental and far-reachiog principles in all of science. 7 LEARNING GOALS By studying this duJpter. you willll!tlm: How to use the concept of gravita-tional potential energy in problems that involve vertical motion. How to use the concept of elastic potential energy in problems that involve a moving body attached to a stretched or compressed spring. The distinction between conserva-tive and nonconservative forces, and how to solve problems in which both kinds of forces act on a moving body. How to calculate the properties of a conservative force if you know the corresponding potential-€nergy function. How to use energy diagrams to understand the motion of an object moving in a straight line under the influence of a conservative force. 213
214 CHAPTER 7 Potential Energy and Energy Conservation 7.1 As a basketball descends, gravitational potential energy is converted to kinetic energy and the basketball's speed increases.