Chapter 7 Problem 40

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Problem

diagram

The force on a particle, acting along the x axis, varies as shown. Determine the work done by this force to move the particle along the x axis:

(a) from x = 0.0 to x = 10.0 m;

(b) from x = 0.0 to x = 15.0 m

Solution

(a)

From x = 0.0 to x = 10.0 m, the shape under the graph is trapezoidal. The area is

(b)

From x = 10.0 m to x = 15.0 m, the force is in the opposite direction from the direction of motion, and so the work will be negative. Again, since the shape is trapezoidal, we find

thus the total work done is 2800 J - 700 J = 2100 J