| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod or block on rough surface in limiting equilibrium (no wall) |
| Difficulty | Standard +0.3 This is a standard M2 moments question requiring taking moments about a point, resolving forces, and applying limiting equilibrium. The geometry is straightforward, and the method is routine for this topic—slightly easier than average due to the guided structure and standard techniques, though the multi-step nature prevents it from being trivial. |
| Spec | 3.03v Motion on rough surface: including inclined planes3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_2}
Figure 2 shows a uniform rod $AB$, of mass $m$ and length $2a$, with the end $B$ resting on rough horizontal ground. The rod is held in equilibrium at an angle $\theta$ to the vertical by a light inextensible string. One end of the string is attached to the rod at the point $C$, where $AC = \frac{2}{3}a$. The other end of the string is attached to the point $D$, which is vertically above $B$, where $BD = 2a$.
\begin{enumerate}[label=(\alph*)]
\item By taking moments about $D$, show that the magnitude of the frictional force acting on the rod at $B$ is $\frac{1}{2}mg \sin \theta$ [3]
\item Find the magnitude of the normal reaction on the rod at $B$. [5]
\end{enumerate}
The rod is in limiting equilibrium when $\tan \theta = \frac{4}{3}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the coefficient of friction between the rod and the ground. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2014 Q5 [11]}}