| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with string support |
| Difficulty | Standard +0.3 This is a standard M3 statics problem involving two-rod systems with straightforward resolution of forces and moments. Part (i) requires basic equilibrium equations (horizontal forces and moments about A), while part (ii) applies the same principles to the second rod. The geometry is given explicitly, eliminating any challenging trigonometry, and the solution path is routine for students who have practiced connected rod problems. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
\includegraphics{figure_2}
Two uniform rods, $AB$ and $BC$, are freely jointed to each other at $B$, and $C$ is freely jointed to a fixed point. The rods are in equilibrium in a vertical plane with $A$ resting on a rough horizontal surface. This surface is $1.5$ m below the level of $B$ and the horizontal distance between $A$ and $B$ is $3$ m (see diagram). The weight of $AB$ is $80$ N and the frictional force acting on $AB$ at $A$ is $14$ N.
\begin{enumerate}[label=(\roman*)]
\item Write down the horizontal component of the force acting on $AB$ at $B$ and show that the vertical component of this force is $33$ N upwards. [4]
\item Given that the force acting on $BC$ at $C$ has magnitude $50$ N, find the weight of $BC$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR M3 2009 Q2 [8]}}