As shown in the figure, a block weighing 10 N travels down a smooth curved track AB connected to a rough horizontal surface. The coefficient of friction between the block and the rough surface is 0.20 . If the block begins slipping on the track from a point 1.0 m above the horizontal surface, determine how far it will move on the rough surface.

Step-by-step solution

Given weight of the block, W = mg = 10 N Height of the track, h = 1.0 m Coefficient of friction, = 0.20 By the work-energy theorem, the net work done on the block is equal to its change in kinetic energy. Since the block starts from rest and finally comes to rest, the change in kinetic energy is zero, K = 0 . The work done by gravity as the block descends is: W_g = mgh = 10 1.0 = 10 J The work done by friction on the rough horizontal surface is: W_f = - mg d = -0.20 10 d = -2d Applying the work-energy theorem: W_g