| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Folded lamina |
| Difficulty | Challenging +1.2 This is a standard M2 centre of mass question involving a folded lamina with two parts: (a) showing a given result for the centre of mass position using composite bodies, and (b) applying equilibrium conditions with moments. While it requires careful coordinate geometry and the folded lamina setup adds some complexity, the techniques are routine for M2 students who have practiced this topic. The 'show that' format in part (a) provides guidance, and part (b) is a straightforward application of the equilibrium principle once part (a) is established. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{52966963-2e62-4361-bcd5-a76322f8621e-08_1141_810_287_148}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{52966963-2e62-4361-bcd5-a76322f8621e-08_752_803_484_1114}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
The uniform triangular lamina $A B C$, shown in Figure 1, has height $9 y$, base $B C = 6 x$, and $A B = A C$
The points $P$ and $Q$ are such that $A P : P C = A Q : Q B = 2 : 1$\\
The lamina is folded along $P Q$ to form the folded lamina $F$\\
The distance of the centre of mass of $F$ from $P Q$ is $d$
\begin{enumerate}[label=(\alph*)]
\item Show that $d = \frac { 16 } { 9 } y$
The folded lamina is suspended from $P$ and hangs freely in equilibrium with $P Q$ at an angle $\alpha$ to the downward vertical.\\
Given that $\tan \alpha = \frac { 64 } { 81 }$
\item find $x$ in terms of $y$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2023 Q3 [8]}}