| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Standard +0.3 This is a standard M2 moments equilibrium problem with typical structure: identifying smooth contact forces, taking moments about a point, and applying friction conditions. While it requires multiple steps and careful geometry with the angle, the techniques are routine for M2 students (resolving forces, taking moments, friction inequality). The algebra is straightforward and the problem follows a predictable pattern for this topic. |
| Spec | 3.03v Motion on rough surface: including inclined planes3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_2}
Figure 2
A uniform rod $AB$ has length $4a$ and weight $W$. A particle of weight $kW$, $k < 1$, is attached to the rod at $B$. The rod rests in equilibrium against a fixed smooth horizontal peg. The end $A$ of the rod is on rough horizontal ground, as shown in Figure 2. The rod rests on the peg at $C$, where $AC = 3a$, and makes an angle $\alpha$ with the ground, where $\tan \alpha = \frac{1}{3}$. The peg is perpendicular to the vertical plane containing $AB$.
\begin{enumerate}[label=(\alph*)]
\item Give a reason why the force acting on the rod at $C$ is perpendicular to the rod. [1]
\item Show that the magnitude of the force acting on the rod at $C$ is
$$\frac{\sqrt{10}}{5}W(1 + 2k)$$ [4]
\end{enumerate}
The coefficient of friction between the rod and the ground is $\frac{3}{4}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that for the rod to remain in equilibrium $k \leq \frac{2}{11}$. [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2015 Q6 [12]}}