Physics C: Mech · FRQ Trainer

A block of mass m is released from rest at the top of a curved, frictionless ramp of height h. At the bottom, it enters a rough horizontal surface with a position-dependent coefficient of kinetic friction μ_k(x) = cx, where c is a positive constant and x is the distance along the rough surface. (a) Derive an expression for the speed of the block at the bottom of the ramp. (b) Set up, but do not evaluate, an integral expression to find the total distance D the block travels on the rough surface before coming to rest. (c) Determine D in terms of m, g, h, and c.