# 6-2 WORK

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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 ev • y meaning of work-any activity that requires muscular or me effort.

In work has a much more precise definition. By making use . ‘on we’ll find that in any motion, no matter how comp liork done on a particle by all forces that act on it equals ts-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. So the ideas of work and kinetic energy will enable us to solve problems in mechanics that we could not have attempted before.

We’ll develop the relationship between work and kinetic energy in Section 6-3, and see what to do with non-constant forces in Section 6–4. Meanwhile, let’s 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 a useful one in such problems.

The three examples of work described above-pulling a sofa, lifting encyclopedias, and pushing a car-have something in common. In each case you do work by exerting aforce on a body while that body moves from one place to another, that is, undergoes a displacement. You do more work if the force is greater (you pull harder on the sofa) or if the displacement is greater (you pull the sofa farther across the room).

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 with magnitude F acts on it in the same direction as the displacement (Fig. 6-1). We define the work W done by a constant force F acting on the body under these conditions as

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.

CAUTION ~ Don’t confuse W (work) with w (weight). Though the symbols may be almost the same, work and weight are different quantities.

The SI unit of work is the joule (abbreviated J, pronounced “jewel,” and named in honor of the nineteenth century English physicist James Prescott Joule). From Eq. (6-1) we see that in any system of units, the unit of work is the unit of force multiplied by the unit of distance. In SI units the unit of force is the newton and the unit of distance is the meter, so one joule is equivalent to one newton-meter (N • m):

1 joule= (1 newton)(1 meter) or 1 J = 1 N.m.

In the British system the unit of force is the pound (lb), the unit of distance is the foot, and the unit of work is thefoot-pound (ft -Ib). The following conversions are useful:

1 J = 0.7376 ft.Ib, 1 ft . Ib = 1.356 J.