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  4. A small slider of mass m is released from rest while in position A and then slides along the vertical-plane track. The track is smooth from A to D and rough (coefficient of kinetic friction μk=(1/√3) ) from point D onwards. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/0a72136e3e214ef13dbac3bfc09782b0-.png /> The distance s traveled along the incline past point D before the slider stops is n R. Find n.

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Q. A small slider of mass $m$ is released from rest while in position $A$ and then slides along the vertical-plane track. The track is smooth from $A$ to $D$ and rough (coefficient of kinetic friction $\mu_{k}=\frac{1}{\sqrt{3}}$ ) from point $D$ onwards.
image
The distance $s$ traveled along the incline past point $D$ before the slider stops is $n R$. Find $n$.

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Solution:

$\frac{1}{2} m v_{D}^{2}=m g\left(d \sin 30^{\circ}\right)+\left(\mu m g \cos 30^{\circ}\right) d$
$\because v_{D}=v_{B} $
$\Rightarrow d=2 R$