$(15$ points$)$ A $10$ kg block starting at rest is released from position A $,$ as seen in the figure below. The track is frictionless except for the portion between points $B$ and C $,$ which has a length of $6\mathrm{.}00$ m $.$ The block travels down the track, hits a spring with spring constant $2,250\frac{N}{m},$ and compresses the spring $0\mathrm{.}300$ m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and rough surface of the track between points $B$ and $C.$

$($A$)1$