| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on inclined plane |
| Difficulty | Standard +0.3 This is a standard statics problem requiring resolution of forces and taking moments about a point. Part (a) involves a straightforward moment calculation about point A to find the normal reaction at B. Part (b) requires resolving forces horizontally and vertically to find the resultant contact force at A. While it involves multiple steps and careful angle work, it follows a well-established method taught in all mechanics courses with no novel insight required. The 'show that' format in part (a) provides confirmation of the correct approach, making this slightly easier than average. |
| Spec | 3.03e Resolve forces: two dimensions3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_11}
A uniform rod $AB$, of weight $20 \text{N}$ and length $2.8 \text{m}$, rests in equilibrium with the end $A$ in contact with rough horizontal ground and the end $B$ resting against a smooth wall inclined at $55°$ to the horizontal. The rod, which rests in a vertical plane that is perpendicular to the wall, is inclined at $30°$ to the horizontal (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Show that the magnitude of the force acting on the rod at $B$ is $9.56 \text{N}$, correct to 3 significant figures. [3]
\item Determine the magnitude of the contact force between the rod and the ground. Give your answer correct to 3 significant figures. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q11 [8]}}