# Work and Kinetic Energy

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Some problems are harder than they look. Suppose you try to find the speed of an arrow that has been shot from a bow. You apply Newton’s laws and all the problem-solving techniques that we’ve learned, but you run across a major stumbling block: After the archer releases the arrow, the bow string exerts a varying force that depends on the arrow’s position. As a result, the simple methods that we’ve learned aren’t enough to calculate the speed. Never fear; we aren’t by any means finished with mechanics, and there are other methods for dealing with such problems.

The new method that we’re about to introduce uses the ideas of work and energy. The applications of these ideas go far beyond mechanics, however. The importance of the energy idea stems from the principle of conservation of energy: Energy is a quantity that can be converted from one form to another but cannot be created or destroyed. In an automobile engine, chemical energy stored in the f1el is converted partially to the energy of the automobile’s motion and partially to thermal energy. In a microwave oven, electromagnetic energy obtained from your power company is converted to thermal energy of the food being cooked. In these and all other processes, the total energy-the sum of all energy present in all different forms-remains the same. No exception has ever been found.

We’ll use the energy idea throughout the rest of this book to study a tremendous range of physical phenomena. This idea will help you understand why a sweater keeps you warm, how a camera’s flash unit can produce a short burst of light, and the meaning of Einstein’s famous equation E = me’.

In this chapter, though, our concentration will be on mechanics. We’ll learn about one important form of energy called kinetic energy, or energy of motion, and how it relates to the concept of work. We’ll also consider power, which is the time rate of doing work. In Chapter 7 we’ll expand the ideas of work and kinetic energy into an understanding of the general concept of energy, and we’ll see how the conservation of energy arises.

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