• An object of mass m is released from rest at height 3R above the ground and slides down the frictionless vertical track as shown. The corner is a frictionless quarter-circle track of radius R. At the end of the quarter-circle track, it enters a horizontal track at x = 0. The coefficient of kinetic friction along the horizontal section increases according to µ(x) = Ax, where A is a positive constant. The block slides and comes to rest at x = d.
• (a) What is the normal force of the quarter-circle track on the block as a function of θ, the angle shown in the diagram? Express your answer in terms of m, R, θ, and g as needed.
• (b) Calculate the distance d that the block slides along the horizontal track before coming to a rest. Express your answer in terms of m, R, A, and g as needed.