Question

Find the work done for the force-displacement plot shown below.

Answer 1

Since work done is scalar product of force and displacement, it can be calculated as area under the force-displacement plot.

So, up to $x_1$ displacement, work done, ${\text{W}}_1$​ = $\frac{(30\times 4)}{2}=60\text{J}$

But after, $x_1$​, the direction of force is reversed.
So, work done, ${\text{W}}_2$​​ = $\frac{\left(\right(45-30)\times (-2\left)\right)}{2}=-15\text{J}$
Hence, total work done = ${\text{W}}_1$​​ $+{\text{W}}_2$ $=60+(-15)=45\text{J}$