Question

A block weighing 10 N travels down a smooth curved 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 the track from a point 1⋅0 m above the horizontal surface, how far will it move on the rough surface?
Figure

Answer 1

Given,
$$\begin{gathered} Weightoftheblock,mg=10\mathrm{N} \\ \mathrm{Friction}\mathrm{coefficient},\mu =0.2 \\ \mathrm{Initial}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{block},H=1\mathrm{m} \\ \mathrm{Initial}\mathrm{velocity}=\mathrm{Final}\mathrm{velocity}=0 \end{gathered}$$

Potential energy of the block at the top of the curved track = Kinetic energy of the block at the bottom of the track
$\Rightarrow K.E.=mgh=10\times 1=10\mathrm{J}$

Again on the horizontal surface the frictional force,
$\mathrm{F}=\mu \mathrm{R}=\mu mg=10\times 1=10\mathrm{J}$

So, the K.E. is used to overcome friction.

$\Rightarrow S=\frac{W}{F}=\frac{10}{2}=5\mathrm{m}$

The block stops after covering 5 m on the rough surface.