If a body has a potential energy of $\left(4 x^2+2 x\right) J$ at a height of $2 \mathrm{~m}$, then the…
If a body has a potential energy of $\left(4 x^2+2 x\right) J$ at a height of $2 \mathrm{~m}$, then the force acting on the body is
$9 \mathrm{~N}$
$27 \mathrm{~N}$
$18 \mathrm{~N}$
$0 \mathrm{~N}$
Solution
Potential energy, $U=\left(4 x^2+2 x\right) J$
Force, $\mathrm{F}=\frac{\mathrm{dU}}{\mathrm{dx}}$
$\begin{aligned} & F=\frac{d}{d x}\left(4 x^2+2 x\right)=8 x+2 \\ & \text { at } x=82 m \\ & F=18 N\end{aligned}$
The force acting on the body is $18 \mathrm{~N}$.