A 0.50-kg block, starting at rest, slides down a 30.0° incline with kinetic friction coefficient 0.30 (the figure below). After sliding 84 cm down the incline, it slides across a frictionless horizontal surface and encounters a spring (k = 33 N/m).

Question

(a) What is the maximum compression of the spring?
cm

(b) After the compression of part (a), the spring rebounds and shoots the block back up the incline. How far along the incline does the block travel before coming to rest?
cm

I am totally lost on this one please help thnks

Answer 1

(a) Potential energy loss = Work done against friction + compressed spring potential energy at maximum compression

M g*(84 sin 30) = M*g*cos30*Uk*84 + (1/2) kX^2

Solve for X.

(b) Use the same approach to compute the gravitational potential energy gain M g Y on the return trip. Y is the amount that it rises and Y/sin30 = 2Y is how far it slides back up.

M g Y = M g cos30*(2Y)*Uk + (1/2) k X^2

Uk is the kinetic friction coefficient.