Question

A particle moves along the $x-$axis from $x=5m$ to $x=12m$ under the influence of a force $F\left(x\right)=\frac{200}{2+x}$. The total work done by this force during this displacement is $200$ in $\alpha$. Find $\alpha$?

Answer 1

The force is given so the work done is displacement from $x=5mtox=12m$is given as,

$dW=F.ds$

So total work done is integration from x = 5m to x 12m

We get

$W={\int }_5^{12}\left(\frac{200}{2+x}\right)$

$=200\ln \left(2+x\right)$

$=138J$