Question

Potential energy curve (sinusoidal) is shown graphically for a particle. The potential energy does not depend on $y$ and $z$ coordinates. The maximum value of corresponding conservative force (in magnitude) for range $0<x<2$ is $n\pi$ (in newton). Find the value of $n$ .

Answer 1

Answer: 3

From the graph,
$U=3sin\pi x+3$ .
Now, take idea from the conservative force. It says that the differentiation of potential energy with respect to displacement is equal to conservative force,
$\therefore F=-\frac{\partial U}{dx}=-3\pi cos\pi x$
$\therefore F_{max}=3\pi \Rightarrow 3\times 3.14=9.42$