A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A ro

Question

A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium and at rest Assuming that all surfaces are smooth, the potential energy stored in the spring is :

Professor PC Thomas Classes · Answer

Rod equilibrium (vertical): $N \cos 	heta = mg \implies N = \frac{mg}{\cos 	heta}$. Wedge equilibrium (horizontal): Spring force balances horizontal component of normal force $\implies kx = N \sin 	heta = \left(\frac{mg}{\cos 	heta}ight) \sin 	heta = mg 	an 	heta \implies x = \frac{mg 	an 	heta}{k}$. Spring Potential Energy: $U = \frac{1}{2}kx^2 = \frac{1}{2}k \left(\frac{mg 	an 	heta}{k}ight)^2 = \frac{m^2g^2 	an^2 	heta}{2k}$