A track consists of a frictionless arc XY, which is a quarter-circle of radius R, and a rough horizontal section YZ. Block A of mass M is released from rest at point X, slides down the curved section of the track, and collides instantaneously and inelastically with identical block B at point Y. The two blocks move together to the right, sliding past point P, which is a distance l from point Y. The coefficient of kinetic friction between the blocks and the horizontal part of the track is µ. Express your answers in terms of M, l, µ, R, and g.
a.) Determine the speed of the block A just before it hits block B.
b.) Determine the speed of the combined blocks immediately after the collision.
c.) Determine the amount of kinetic energy lost due to the collision.
d.) The specific heat of the material used to make the blocks is c. Determine the temperature rise that results from the collision in terms of c and the other given quantities. (assume that no energy is transferred to the track or to the air surrounding the blocks).
