A block of mass m is positioned on the frictionless semi-circular surface with radius R as shown. It slides down the surface and undergoes a completely inelastic collision with an identical block which is at rest at the bottom. After the collision, both blocks slide up a ramp that makes an angle ? with the horizontal until they come to rest. The coefficient of kinetic friction between the blocks and the ramp is ?k. Find expressions for the following:

(a) The block?s speed immediately before the collision (in terms of g and R only),

(b) The combined speed of the two blocks immediately after the collision (in terms of g and R only),

(c) The thermal energy generated by the blocks as they slide up the ramp (in terms of ?k, m, g, h and a trigonometric function of ? only),

(d) The height h of the blocks on the ramp when they come to rest. Your expression should be fully simplified, and don?t forget to do a consistency check of some sort.

m m R 0 : h