Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 35_H

In Fig. 8.25, a block of mass \( m = 3.20 \text{ kg} \) slides from rest a distance \( d \) down a frictionless incline at angle \( \theta = 30.0^\circ \) where it runs into a spring of spring constant \( 431 \text{ N/m} \). When the block momentarily stops, it has compressed the spring by \( 21.0 \text{ cm} \). What are (a) distance \( d \) and (b) the distance between the point of the first block–spring contact and the point where the block’s speed is greatest?