8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-24_346_961_246_543}
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\caption{Figure 5}
\end{figure}
A fixed rough plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 5 } { 12 }\)
A small smooth pulley is fixed at the top of the plane.
One end of a light inextensible string is attached to a particle \(P\) which is at rest on the plane. The string passes over the pulley and the other end of the string is attached to a particle \(Q\) which hangs vertically below the pulley, as shown in Figure 5.
Particle \(P\) has mass \(m\) and particle \(Q\) has mass \(0.5 m\)
The string from \(P\) to the pulley lies along a line of greatest slope of the plane.
The coefficient of friction between \(P\) and the plane is \(\mu\).
The system is in limiting equilibrium with the string taut and \(P\) is on the point of slipping up the plane.
- Find the value of \(\mu\).
The string breaks and \(P\) begins to move down the plane.
When particle \(P\) has travelled a distance of 0.8 m down the plane, the speed of \(P\) is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) - Find the value of \(V\).