How to solve problems involving power the rate of doing work 181 182 CHAPTER 6

# How to solve problems involving power the rate of

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How to solve problems involving power (the rate of doing work). 181 182 CHAPTER 6 Work and Kinetic Energy 6.1 These people are doing work as they push on the stalled car because they exert a force on the car as it moves. 6.2 The work done by a constant force acting in the same mrection as the dis- placement. If a body moves through a displacement t while a constant force F acts on it - l== ;;.I - X ... the work done by the force on the body is W = Fs. 6.1 Work You'd probably agree that it's hard work to pull a heavy sofa across the room, to lift a stack of encyclopedias from the floor to a high shelf, or to push a stalled car off the road. Indeed, all of these examples agree with the everyday meaning of work---mly activity that requires muscular or mental effort. In physics, work has a much more precise definition. By making use of this definition we'll find that in any motion, no matter how complicated, the total work done on a particle by all forces that act on it equals the change in its kinetic energy-a quantity that's related to the particle's speed. This relationship holds even when the forces acting on the particle aren't constant, a situation that can be difficult or impossible to handle with the techniques you learned in Chapters 4 and 5. The ideas of work and kinetic energy enable us to solve problems in mechanics that we could not have attempted before. In this section we'll see how work is defined and how to calculate work in a variety of situations involving constant forces. Even though we already know how to solve problems in which the forces are constant, the idea of work is still useful in such problems. Later in this chapter we'll relate work and kinetic energy, and then apply these ideas to problems in which the forces are not constant. The three examples of work described above-pulling a sofa,lifting encyclo- pedias, and pushing a car-have something in common. In each case you do work by exerting a force on a body while that body moves from one place to another---that is, undergoes a displacement (Fig. 6.1). You do more work if the force is greater (you push harder on the car) or if the displacement is greater (you push the car farther down the road). The physicist's definition of work is based on these observations. Consider a body that undergoes a displacement of magnitude s along a straight line. (For now, we'll assume that any body we discuss can be treated as a particle so that we can ignore any rotation or changes in shape of the body.) While the body moves, a constant force F acts on it in the same direction as the displacement -; (Fig. 6.2). We define the work W done by this constant force under these circumstances as the product of the force magnitude F and the displacement magnitude s: W=Fs (constant force in direction of straight-line displacement) (6.1) The work done on the body is greater if either the force F or the displacement s is greater, in agreement with our observations above .  • • • 