A 4-kg object sliding at speed 5 m/s along a smooth horizontal surface encounters a rough surface, 1.5 meters wide. The coefficient of kinetic friction over the rough surface is 0.20. After leaving the rough surface, the object continues over smooth surface until it strikes the ends of a horizontally-aligned spring, whose spring constant is 200 N/m, and whose opposite end is attached to a wall. What will be the maximum compression of the spring, in meters?
The Attempt at a Solution
I know this must be a conservation of energy problem.
0.5 mv2 + 0.5 kx2 = 0.5 mv02 + 0.5 kx02
But since friction is involved, I'm not sure how to incorporate it.