\includegraphics{figure_2}

Figure 2 shows two particles $A$ and $B$, of masses $3m$ and $4m$ respectively, attached to the ends of a light inextensible string. Initially $A$ is held at rest on the surface of a fixed rough inclined plane. The plane is inclined to the horizontal at an angle $\alpha$ where $\tan \alpha = \frac{3}{4}$. The coefficient of friction between $A$ and the plane is $\frac{1}{4}$. The string passes over a small smooth light pulley $P$ which is fixed at the top of the plane. The part of the string from $A$ to $P$ is parallel to a line of greatest slope of the plane. The particle $B$ hangs freely and is vertically below $P$. The system is released from rest with the string taut and with $B$ at a height of 1.75 m above the ground. In the subsequent motion, $A$ does not hit the pulley.

For the period before $B$ hits the ground,

\begin{enumerate}[label=(\alph*)]
\item write down an equation of motion for each particle.
[4]
\item Hence show that the acceleration of $B$ is $\frac{8}{35}g$.
[5]
\item Explain how you have used the fact that the string is inextensible in your calculation.
[1]
\end{enumerate}

When $B$ hits the ground, $B$ does not rebound and comes immediately to rest.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the distance travelled by $A$ from the instant when the system is released to the instant when $A$ first comes to rest.
[7]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2017 Q7 [17]}}