Chapter 6.6, Problem 3E

To determine

To find work done use by the given graph.

Answer to Problem 3E

Work done is $180\text{Jouls}$

Explanation of Solution

Given information: Given the distance $8m$

Calculation:

Work this is the integral of force F with respect to displacement $x$ .

The answer has units of Newton meters (also known as jouls).

For this problem, we can integrate by fixling the area under the curve from $x=0\text{ to }x=8$ .

The area is a trapezoid so $A=\left(\frac{b_1+b_2}{2}\right)h$

  $\begin{array}{l}W={\displaystyle \int A\left(x\right)}dx\\ =\left(\frac{4+8}{2}\right)30N\\ =180N.m\\ =180J\end{array}$

Thus, the Work done is $180\text{Jouls}$