Chapter 9, Problem 75AP

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 m₁, moves to the right with speed v₁, and the second glider, of mass m₂, moves more slowly to the right with speed v₂. When m₁ collides with the spring attached to m₂, the spring compresses by a distance x_max, and the gliders then move apart again. In terms of v₁, v₂, m₁, m₂, and k, find (a) the speed v at maximum compression, (b) the maximum compression x_max, and (c) the velocity of each glider after m₁ has lost contact with the spring.

Figure P9.41