Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_44

2/44 The situation of Prob. 2/43 is repeated here. This time, use the values \( m = 5 \text{ kg} \), \( k = 150 \text{ N/m} \), \( \mu = 0.40 \), and \( x_0 = 500 \text{ mm} \) and determine the final spring stretch (or compression) \( x_f \) when the block comes to a complete stop. (Note: The sign on the \( \mu g \) term is dictated by the direction of motion for the block and always acts in the direction opposite velocity.) From Prob. 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.