Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_43

2/43 A block of mass \(m\) rests on a rough horizontal surface and is attached to a spring of stiffness \(k\). The coefficients of both static and kinetic friction are \(\mu\). The block is displaced a distance \(x_0\) to the right of the unstretched position of the spring and released from rest. If the value of \(x_0\) is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration \(a = \mu g - \frac{k}{m}x\), where \(x\) represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values \(m = 5 \text{ kg}\), \(k = 150 \text{ N/m}\), \(\mu = 0.40\), and \(x_0 = 200 \text{ mm}\) and determine the final spring stretch (or compression) \(x_f\) when the block comes to a complete stop.