4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6d100ff-dd4a-4591-a0a3-81761773045e-07_544_1264_251_338}
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\caption{Figure 1}
\end{figure}
Two particles \(P\) and \(Q\), of mass 2 kg and 4 kg respectively, are connected by a light inextensible string. Initially \(P\) is held at rest at the point \(A\) on a rough fixed plane inclined at \(\alpha\) to the horizontal ground, where \(\sin \alpha = \frac { 3 } { 5 }\). The string passes over a small smooth pulley fixed at the top of the plane. The particle \(Q\) hangs freely below the pulley and 2.5 m above the ground, as shown in Figure 1. The part of the string from \(P\) to the pulley lies along a line of greatest slope of the plane. The system is released from rest with the string taut. At the instant when \(Q\) hits the ground, \(P\) is at the point \(B\) on the plane. The coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 4 }\).
- Find the work done against friction as \(P\) moves from \(A\) to \(B\).
- Find the total potential energy lost by the system as \(P\) moves from \(A\) to \(B\).
- Find, using the work-energy principle, the speed of \(P\) as it passes through \(B\).