| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| 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 two-rod statics problem requiring moment equilibrium and force resolution. The geometry is straightforward (vertical alignment given), and the method is routine: take moments about A, then resolve forces. While it requires careful bookkeeping of forces and multiple steps, it follows a standard M3 template with no novel insight needed—slightly easier than average A-level. |
| 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 of equal length and each has weight $100$ N. The rods are freely jointed to each other at $B$, and $A$ is freely jointed to a fixed point. The rods are in equilibrium in a vertical plane with $AB$ horizontal and $C$ resting on a rough horizontal surface. $C$ is vertically below the mid-point of $AB$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item By taking moments about $A$ for $AB$, find the vertical component of the force on $AB$ at $B$. Hence find the vertical component of the contact force on $BC$ at $C$. [3]
\item Calculate the magnitude of the frictional force on $BC$ at $C$ and state its direction. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR M3 2010 Q2 [7]}}