Chapter 7 Problem 40

Problem

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

$W_{a}=\left(400{\text{ N}}\right){\frac {1}{2}}\left(10{\text{ m}}+4{\text{ m}}\right)=2800{\text{ J}}$

(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

$W_{b}=\left(-200{\text{ N}}\right){\frac {1}{2}}\left(5{\text{ m}}+2{\text{ m}}\right)=-700{\text{ J}}$

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