Question

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface as shown in figure below. 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? (Assume g = 10 m/sec${}^2$)

• A. 10 m
• B. 12 m
• C. 2 m
• D. 5 m

Answer 1

The correct option is D 5 m

Using conservation of mechanical energy between points A and B

$m\times g\times 1=\frac{1}{2}m{V}^2$

$\Rightarrow$ $V^2=2g$

$V=\sqrt{20}m/s$

Now by applying basic kinematic equation after point B we get

$V_f^2=U^2+2as$

$V_f=0$

$U=V=\sqrt{20}$

$a=\mu g=0.2\times 10=2m/s^2$

$S=\frac{U^2}{2a}=\frac{{\left(\sqrt{20}\right)}^2}{2\times 0.2\times 10}=5m$