4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e6d100ff-dd4a-4591-a0a3-81761773045e-07_544_1264_251_338}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\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 $\frac { 1 } { 4 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the work done against friction as $P$ moves from $A$ to $B$.
\item Find the total potential energy lost by the system as $P$ moves from $A$ to $B$.
\item Find, using the work-energy principle, the speed of $P$ as it passes through $B$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2016 Q4 [11]}}