A block of mass m compresses a spring (spring constant k) by a distance of d and starts from rest. It is launched from the spring and over the rough patch (length L and coefficient of kinetic friction μk) and then over the frictionless hill, which has a radius of curvature R at the top, as shown.

What is the normal force on the mass at point B? Put your answer in terms of m, k, d, μk, L, g, and R.

What is the shortest length L of the friction patch that is possible in order to make sure the block does not lose contact with the track at point B?