4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{0d5a56ba-6a33-4dc8-b612-d2957211124f-10_410_1143_258_404}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

A boy sees a box on the end $Q$ of a plank $P Q$ which overhangs a swimming pool. The plank has mass 30 kg , is 5 m long and rests in a horizontal position on two bricks. The bricks are modelled as smooth supports, one acting on the rod at $P$ and one acting on the rod at $R$, where $P R = 3 \mathrm {~m}$. The support at $R$ is on the edge of the swimming pool, as shown in Figure 2. The boy has mass 40 kg and the box has mass 2.5 kg . The plank is modelled as a uniform rod and the boy and the box are modelled as particles.

The boy steps on to the plank at $P$ and begins to walk slowly along the plank towards the box.
\begin{enumerate}[label=(\alph*)]
\item Find the distance he can walk along the plank from $P$ before the plank starts to tilt.
\item State how you have used, in your working, the fact that the box is modelled as a particle.

A rock of mass $M \mathrm {~kg}$ is placed on the plank at $P$. The boy is then able to walk slowly along the plank to the box at the end $Q$ without the plank tilting. The rock is modelled as a particle.
\item Find the smallest possible value of $M$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2019 Q4 [9]}}