Question

A wedge of mass ${}^{\prime }{M}^{\prime }$ and angle of inclination ${}^{\prime }{\theta }^{\prime }$ and a block of mass ${}^{\prime }{m}^{\prime }$ are arranged in a manner shown in the figure. The spring of force constant ${}^{\prime }{k}^{\prime }$ is attached to the wedge. Assuming the pulleys to be massless and all surfaces to be frictionless, find the compression of the spring under equilibrium condition.

Answer 1

Force due to gravitation, $F_g=mg\sin \theta$

Force due to spring, $F_s=kx$

$F_s=F_g$

$kx=mg\sin \theta$

$x=\frac{mg\sin \theta }{k}$

Potential energy stored in the spring,

$U=\frac{k{x}^2}{2}=\frac{k(mg\sin \theta {)}^2}{2k^2}=\frac{(mg\sin \theta {)}^2}{2k}$