Question

A position dependent force $F=7-2x+3x^2$ newton (where x is in meter) on a small body of mass 2 Kg & displace it from $x=0$ to $x=5$ m. Calculate the work done.

Answer 1

$\text{Step 1: Work done}$

Work done for small displacement can be defined as:

$dW=Fdx$ $....\left(1\right)$

$\text{Step 2: Integrate the equation}$

Total work done can be calculated by integrating the equation $\left(1\right)$ with limits $x=0$ to $x=5m$

$\int dW=\underset{0}{\overset{5}{\int }}Fdx$

$\int dW=\underset{0}{\overset{5}{\int }}(7-2x+3x^2)dx$

$\Rightarrow W={[7x-\frac{2x^2}{2}+\frac{3x^3}{3}]}_0^5$

$\Rightarrow W=35-25+125=135J$

Hence, the work done is $135J$