\includegraphics{figure_2}

Two particles $P$ and $Q$ have masses 0.3 kg and $m$ kg respectively. The particles are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a fixed rough plane. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac{3}{4}$. The coefficient of friction between $P$ and the plane is $\frac{1}{2}$.

The string lies in a vertical plane through a line of greatest slope of the inclined plane. The particle $P$ is held at rest on the inclined plane and the particle $Q$ hangs freely below the pulley with the string taut, as shown in Figure 2.

The system is released from rest and $Q$ accelerates vertically downwards at 1.4 m s$^{-2}$. Find

\begin{enumerate}[label=(\alph*)]
\item the magnitude of the normal reaction of the inclined plane on $P$, [2]

\item the value of $m$. [8]
\end{enumerate}

When the particles have been moving for 0.5 s, the string breaks. Assuming that $P$ does not reach the pulley,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the further time that elapses until $P$ comes to instantaneous rest. [6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2011 Q6 [16]}}