Question #42614

A block of mass $m = 1 \text{ kg}$ is attached to a fixed wall by a light spring of force constant $k = 100 \text{ N/m}$. The block rests on a horizontal surface. The natural length of the spring is at $x = 0$. The surface is perfectly smooth for $x \ge 0.16 \text{ m}$ and rough for $x < 0.16 \text{ m}$ with a coefficient of kinetic friction $\mu_k = 0.2$. A stationary block of mass $M = 3 \text{ kg}$ is placed exactly at the boundary $x = 0.16 \text{ m}$. Block $m$ is pulled to $x = 0.20 \text{ m}$ and released from rest. When it reaches $x = 0.16 \text{ m}$, it undergoes a perfectly inelastic collision with block $M$, and they stick together. Find the maximum compression of the spring during the subsequent motion. (Take $g = 10 \text{ m/s}^2$)