Serway & Jewett — Oscillatory Motion: Problem 32

Review. This problem extends the reasoning of Problem 41 in Chapter 9. Two gliders are set in motion on an air track. Glider 1 has mass \(m_1 = 0.240 \text{ kg}\) and moves to the right with speed \(0.740 \text{ m/s}\). It will have a rear-end collision with glider 2, of mass \(m_2 = 0.360 \text{ kg}\), which initially moves to the right with speed \(0.120 \text{ m/s}\). A light spring of force constant \(45.0 \text{ N/m}\) is attached to the back end of glider 2 as shown in Figure P9.41. When glider 1 touches the spring, superglue instantly and permanently makes it stick to its end of the spring. (a) Find the common speed the two gliders have when the spring is at maximum compression. (b) Find the maximum spring compression distance. The motion after the gliders become attached consists of a combination of (1) the constant-velocity motion of the center of mass of the two-glider system found in part (a) and (2) simple harmonic motion of the gliders relative to the center of mass. (c) Find the energy of the center-of-mass motion. (d) Find the energy of the oscillation.