Work done by a varriable forse

In many situations the force acting on a particle varies both in magnitude and in direction. In this section we consider cases in which the force and the displace­ment lie along the same line, say, the x axis. We begin by showing that work may be calculated from the area under the F versus x graph.

FIGURE 4.2

Let us first consider the work done by a constant force F = F_x i on a body whose displacement s = ∆x i; that is,

W = F · s = F_x ∆x

The work is positive if F_x and ∆ х are in the same direction, and it is negative if they are in opposite directions. We may represent this work by the area under the graph of F_x versus x. In Fig. 4.2 we have taken F_x = F_o. The work done in a displacement from x _A to x _B is F ₀(x _B− x _A), which is the shaded area in the graph. A displacement from x _B to x _A would mean that the area has a negative sign.

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