Serway & Jewett — Linear Momentum and Collisions: Problem 41

Two gliders are set in motion on a horizontal air track. A light spring of force constant $k$ is attached to the back end of the second glider. As shown in Figure P9.41, the first glider, of mass $m_1$, moves to the right with speed $v_1$, and the second glider, of mass $m_2$, moves more slowly to the right with speed $v_2$. When $m_1$ collides with the spring attached to $m_2$, the spring compresses by a distance $x_{\text{max}}$, and the gliders then move apart again. In terms of $v_1$, $v_2$, $m_1$, $m_2$, and $k$, find (a) the speed $v$ at maximum compression, (b) the maximum compression $x_{\text{max}}$, and (c) the velocity of each glider after $m_1$ has lost contact with the spring.