Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 30

30 A 2.0 kg breadbox on a frictionless incline of angle $\theta = 40^\circ$ is connected, by a cord that runs over a pulley, to a light spring of spring constant $k = 105 \text{ N/m}$, as shown in Fig. 8-31. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction (up or down the incline) of the box’s acceleration at the instant the box momentarily stops?