Serway & Jewett — Energy of a System: Problem 47.

An inclined plane of angle \(\theta = 20.0^\circ\) has a spring of force constant \(k = 500 \text{ N/m}\) fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P7.47. A block of mass \(m = 2.50 \text{ kg}\) is placed on the plane at a distance \(d = 0.300 \text{ m}\) from the spring. From this position, the block is projected downward toward the spring with speed \(v = 0.750 \text{ m/s}\). By what distance is the spring compressed when the block momentarily comes to rest?