Question

Two identical massless springs of constant k = 200N/m are fixed at opposite ends of a level track, as shown. A 5 kg block is pressed against the left spring, compressing it by 0.15m. The block is then released from rest. The entire track is frictionless except for the region of length 0.25m between A and B, where mK = 0.08.

Answer 1

Energy in spring:
E = ½k · x²; where x = 0.15m

From coefficient of friction,
F = µ · N = µ · mg; where m = 5kg and g = 9.807m/s²

Work done each pass =
W = ∫Fdx = Force · distance

Just divide E by W to see how many passes, use this to figure out where it stops.