Question

A block is released from rest from a height $h=5\text{m}$. After travelling through the smooth curved surface, it moves on the rough horizontal surface through a length $l=8\text{m}$ and climbs onto the other smooth curved surface through a height $h^{{}^{\prime }}$. If coefficient of friction of the rough surface is $\mu =0.5$, find $h^{{}^{\prime }}$.

• A. $2\text{m}$
• B. $4\text{m}$
• C. $5\text{m}$
• D. $1\text{m}$

Answer 1

The correct option is D $1\text{m}$

The forces acting on the block are normal reaction by surface ($N$), force due to gravity and friction force ($f$) acting between rough surface and the block.
Applying work energy theorem between initial and final position,
$W_N+W_f+W_{gr}=\Delta KE$
Work done by normal reaction, $W_N=0$
Work done by friction force, $W_f=-\mu mgl$
Work done by gravity, $W_{gr}=mg(h-h^{{}^{\prime }})$
Also, $\Delta KE=0$
($\because$ initial and final velocities are 0 )

Thus, $-\mu mgl+mg(h-h^{{}^{\prime }})=0$
$h^{{}^{\prime }}=h-\mu l=5-\frac{1}{2}\times 8=1\text{m}$