Question

A particle has potential energy dependent on its position on the $x$ axis, represented by the function $U\left(x\right)=e^{2x}+1$ for all real values of $x$, where $U\left(x\right)$ and $x$ are given in standard units. The force it feels at position $x=1$ is closest to
[Take $e=2.72$]

• A. $8.39\text{N}$
• B. $-8.39\text{N}$
• C. $14.8\text{N}$
• D. $-14.8\text{N}$

Answer 1

The correct option is D $-14.8\text{N}$

The potential energy of the particle $U\left(x\right)=e^{2x}+1$
Thus force acting on the particle $F=-\frac{dU\left(x\right)}{dx}=-2e^{2x}\text{N}$
$\Rightarrow {\begin{array}{c}F\end{array}|}_{x=1}=-2e^2=-2\times (2.72{)}^2=-14.8\text{N}$