A 10.0 kg block is released from point A in the figure below. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring of force constant 2350 N/m, and compresses the spring to 0.250 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between B and C.

Answer 1

Use the spring compression to compute the kinetic energy when it hits the spring.
(1/2)MC^2 = (1/2) kX^2
Use that energy to figure out how much energy is lost while traveling from B to C.

Potential energy loss
= kinetic energy gain + frictional work
I suspect you will need information on the slope of the track, which you have not disclosed. It is probably shown on the figure you mentioned. The lost energy is converted to frictional heat, and you can use that to compute the friction coefficient.
Energy lost = friction force x distance

Answer 2

262