$($a$)$ A $15\mathrm{.}0$ kg block is released from rest at point A 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 of force constant $2,350$ N$/$m$,$ and compresses the spring $0\mathrm{.}200$ m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between points $B$ and $C.$

$($b$)$ What If$?$ The spring now expands, forcing the block back to the left. Does the block reach point B$?$

Yes

No

If the block does reach point B$,$ how far up the curved portion of the track does it reach, and if it does not, how far short of point B does the block come to a stop? $($Enter your answer in m$.)$

m