The track in the figure below consists of two frictionless, quarter-circle vertical sections of radius R connected by a flat section of length L. This flat section has coefficients of static and kinetic friction μs and μk respectively. A block of mass M is released from rest at the top of the left side and makes it up a height H (measured vertically from the flat surface) on the right side before coming momentarily to rest and sliding back down again.
A. Solve for H in terms of R, L, M, μs, μk and the acceleration of gravity g. (You might not need all of these factors in your answer.)
B. How many times, N, (in terms of R, L, M, μs, μk and g) will the block traverse the flat section? (A fractional answer for N is fine; it tells you where along L the block stops on its last trip.) Check that your answer makes sense if μk → 0.