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  4. A block is released from rest from a height h = 5 m. After travelling through the smooth curved surface it moves on the rough horizontal surface through a length l = 8 m and climbs onto the other smooth curved surface through a height h'. If μ=0.5,, find h' <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/7e3eb40343fce2c46d676522f2f0d977-.png />

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Q. A block is released from rest from a height $h = 5\, m.$ After travelling through the smooth curved surface it moves on the rough horizontal surface through a length $l = 8\, m$ and climbs onto the other smooth curved surface through a height $h'$. If $\mu=0.5,$, find $h'$
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Work, Energy and Power

Solution:

The forces acting on the block and $N$, gravity and friction
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$W_{f}+W_{f}+W_{ gr }= DK$
Where $W_{N}=0, W_{f}=-\mu mgl$
and $W_{ gr }=m g\left(h-h'\right)$
and $\Delta K=0$
Thus, $-\mu m g l +m g\left(h-h'\right)=0$
$h'=h-\mu l=5-\frac{1}{2} \times 8=1\, m$