| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with rough contact at free end |
| Difficulty | Standard +0.3 This is a standard M2 moments equilibrium problem requiring taking moments about a point, resolving forces vertically and horizontally, and using given trigonometry. The multi-part structure guides students through the solution systematically. While it involves several steps and careful bookkeeping of forces, it follows a routine mechanics approach without requiring novel insight or particularly challenging problem-solving. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_2}
Figure 2 shows a horizontal uniform pole $AB$, of weight $W$ and length $2a$. The end $A$ of the pole rests against a rough vertical wall. One end of a light inextensible string $BD$ is attached to the pole at $B$ and the other end is attached to the wall at $D$. A particle of weight $2W$ is attached to the pole at $C$, where $BC = x$. The pole is in equilibrium in a vertical plane perpendicular to the wall. The string is inclined at an angle $θ$ to the horizontal, where $\tan θ = \frac{5}{3}$. The pole is modelled as a uniform rod.
\begin{enumerate}[label=(\alph*)]
\item Show that the tension in $BD$ is $\frac{5(5a - 2x)}{6a}W$.
[5]
\end{enumerate}
The vertical component of the force exerted by the wall on the pole is $\frac{1}{2}W$. Find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item x in terms of $a$,
[3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item the horizontal component, in terms of $W$, of the force exerted by the wall on the pole.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [12]}}