Question

A block weighing 10 N travels down a smooth track AB joined to a rough horizontal surface (figure 8-E5). The rough surface has a friction coefficient of 0.20 with the block. If the block starts slipping on track from a point 1.0 m above the horizontal surface, how far will it move on the rough surface?

Answer 1

5.0 m

Answer 2

The block's initial potential energy at height $h$ is converted into kinetic energy at the bottom of the smooth track. This kinetic energy is then dissipated as work done against friction on the rough horizontal surface. By equating the initial potential energy to the work done by friction, we find the distance traveled on the rough surface.

Initial potential energy = Work done by friction $mgh = \mu_k mgd$ $h = \mu_k d$ $d = h / \mu_k = 1.0 / 0.20 = 5.0 \, \text{m}$.