| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Toppling on inclined plane |
| Difficulty | Standard +0.3 This is a straightforward M2 centre of mass question requiring Pythagoras verification, standard centroid formula for a right-angled triangle (⅓ from each perpendicular side), and toppling condition (vertical through COM passes through pivot edge). All steps are routine textbook applications with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.04b Find centre of mass: using symmetry6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| (a) PQR is a 3, 4, 5 \(\triangle\) so angle PQR = \(90°\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| - (i) \(\frac{1}{3} \times 24 = 8 \text{ cm}\) from PQ | M1 A1 | |
| - (ii) \(\frac{1}{3} \times 18 = 6 \text{ cm}\) from QR | M1 A1 | |
| (b) Equilibrium is about to be broken when G is above Q | M1 | |
| Then \(\tan \theta = \frac{8}{6}\) | \(\theta = 53.1°\) | M1 A1 A1 |
**(a)** PQR is a 3, 4, 5 $\triangle$ so angle PQR = $90°$ | B1 |
By property of medians, distances are:
- (i) $\frac{1}{3} \times 24 = 8 \text{ cm}$ from PQ | M1 A1 |
- (ii) $\frac{1}{3} \times 18 = 6 \text{ cm}$ from QR | M1 A1 |
**(b)** Equilibrium is about to be broken when G is above Q | M1 |
Then $\tan \theta = \frac{8}{6}$ | $\theta = 53.1°$ | M1 A1 A1 | 9 marks$PQR$ is a triangular lamina with $PQ = 18$ cm, $QR = 24$ cm and $PR = 30$ cm.
\begin{enumerate}[label=(\alph*)]
\item Verify that angle $PQR$ is a right angle and find the distances of the centre of mass of the lamina from \begin{enumerate}[label=(\roman*)] \item $PQ$, \item $QR$. \end{enumerate} [5 marks]
\end{enumerate}
\includegraphics{figure_6}
The lamina is held in a vertical plane and placed on a line of greatest slope of a rough plane inclined at an angle $\theta$ to the horizontal, as shown.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the largest value of $\theta$ for which equilibrium will not be broken by toppling. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q6 [9]}}