Question #42188

A fixed horizontal cylinder of cross-sectional area $A$ contains an ideal gas sealed by a massless, frictionless piston. A solid block of mass $m$ slides on a rough horizontal floor parallel to the cylinder. A rigid, massless rod connects the piston to the block, maintaining a constant angle $\theta$ below the horizontal such that $\tan\theta = 0.5$. The coefficient of kinetic friction between the block and the floor is $\mu_k = 0.5$. Initially, the gas has volume $V_0 = A x_0$ and pressure $P_0 = \frac{2e}{3} \frac{mg}{A}$, where $e$ is the base of the natural logarithm. The system is released from rest and the gas expands isothermally. Assuming the block does not topple, what is the maximum kinetic energy of the block during the expansion?