A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4201 N/m after being compressed a distance x1 = 0.556 m from the spring’s unstretched length. The floor is frictionless except for a rough patch a distance d = 2.3 m long. For this rough path, the coefficient of friction is μk = 0.45.

Question

1) What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?

Answer 1

the energy from the spring equals the work against friction

1/2 k x^2 = m g μ d