Question

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

• A. 75J
• B. 90J
• C. 45J
• D. 150J

Answer 1

The correct option is C

45J

Since work done is scalar product of force and displacement, it can be calculated as area under the force-displacement plot.
Up to $x_1$ displacement, let the work done be $W_1$
$W_1=areaofrightangledtriangle=\frac{b\times h}{2}$

$W_1$​ = $\frac{\left(\right(30-0)\times (4-0\left)\right)}{2}$ = 60 J
But after, $x_1$​, the force becomes negative. Let this work done be $W_2$​​.
$W_2$​​ = $\frac{\left(\right(45-30)\times (-2-0\left)\right)}{2}$ = 15J
Hence, Total work done = $W_1$​​ + $W_2$​​ = 60 + (-15) = 45 J