Problem $20$:

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 $.$ 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 $a=g-\frac{k}{m}x,$

where $x$ represents the amount of stretch $($or compression$)$ in the spring at any given location in the motion. Use the

values $m=5kg,k=150\frac{N}{m},=0\mathrm{.}40,$ and $x_0=200mm$ and determine the final spring stretch $($or

compression$)x_f$ when the block comes to a complete stop.

THE ANSWER IS $61\mathrm{.}6$ mm