| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on inclined plane |
| Difficulty | Standard +0.3 This is a standard M2 statics problem requiring resolution of forces and taking moments about a point to find reactions, followed by applying limiting equilibrium (F = μR). The setup is straightforward with clear geometry, and the method is routine for this topic, making it slightly easier than average for A-level mechanics questions. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| (a) mom. about \(B\): \(6g\cos30° - R.2\cos30° = 0\) | M1 A1 | |
| \(\therefore R = 3g\) | A1 | |
| mom. about \(A\): \(6g\cos30° - S.2 = 0\) | M1 A1 | |
| \(\therefore S = \frac{3}{2}\sqrt{3}g\) | A1 | |
| (b) resolve \(\rightarrow\): \(\mu S\sin60° - S\sin30° = 0\) | M1 A1 | |
| \(\mu = \dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \dfrac{1}{\sqrt{3}}\) | A1 | (9) |
## Question 4:
| Answer/Working | Marks | Notes |
|---|---|---|
| **(a)** mom. about $B$: $6g\cos30° - R.2\cos30° = 0$ | M1 A1 | |
| $\therefore R = 3g$ | A1 | |
| mom. about $A$: $6g\cos30° - S.2 = 0$ | M1 A1 | |
| $\therefore S = \frac{3}{2}\sqrt{3}g$ | A1 | |
| **(b)** resolve $\rightarrow$: $\mu S\sin60° - S\sin30° = 0$ | M1 A1 | |
| $\mu = \dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \dfrac{1}{\sqrt{3}}$ | A1 | **(9)** |
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0ea2267e-6c46-4a4f-9a38-c242de57901d-3_378_730_196_609}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Figure 1 shows a uniform rod $A B$ of length 2 m and mass 6 kg inclined at an angle of $30 ^ { \circ }$ to the horizontal with $A$ on smooth horizontal ground and $B$ supported by a rough peg. The rod is in limiting equilibrium and the coefficient of friction between $B$ and the peg is $\mu$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $g$, the magnitude of the reactions at $A$ and $B$.
\item Show that $\mu = \frac { 1 } { \sqrt { 3 } }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [9]}}