6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-20_234_1357_244_354}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a block $A$ with mass $4 m$ and a block $B$ with mass $5 m$.\\
Block $A$ is at rest on a rough plane inclined at an angle $\alpha$ to the horizontal.\\
Block $B$ is at rest on a rough plane inclined at an angle $\beta$ to the horizontal.\\
The blocks are connected by a light inextensible string which passes over a small smooth pulley at the top of each plane.

A small smooth ring $C$, of mass $8 m$, is threaded on the string between the pulleys so that $A , B$ and $C$ all lie in the same vertical plane.

The part of the string between $A$ and its pulley lies along a line of greatest slope of the plane of angle $\alpha$.

The part of the string between $B$ and its pulley lies along a line of greatest slope of the plane of angle $\beta$.

The angle between the vertical and the string between each pulley and the ring $C$ is $\gamma$.\\
The two blocks, $A$ and $B$, are modelled as particles.\\
Given that

\begin{itemize}
  \item $\tan \alpha = \frac { 5 } { 12 }$ and $\tan \beta = \frac { 7 } { 24 }$ and $\tan \gamma = \frac { 3 } { 4 }$
  \item the coefficient of friction, $\mu$, is the same between each block and its plane
  \item one of the blocks is on the point of sliding up its plane
  \item the tension in the string is $T$
\begin{enumerate}[label=(\alph*)]
\item determine, in terms of $m$ and $g$, an expression for $T$,
\item draw a diagram showing the forces on block $A$, clearly labelling each of the forces acting on the block,
\item determine the value of $\mu$, giving a justification for your answer.\\
\includegraphics[max width=\textwidth, alt={}, center]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-20_2266_50_312_1978}
\end{itemize}
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2024 Q6 [18]}}