| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Horizontal force on slope |
| Difficulty | Challenging +1.2 This is a multi-step statics problem requiring resolution of forces in two directions (parallel and perpendicular to the plane), application of friction law F ≤ μR, and optimization to find the limiting case. While it involves several techniques and careful geometric reasoning about force components, it follows a standard approach for inclined plane friction problems that A-level students practice extensively. The 5 marks and need to find a maximum value elevate it slightly above average difficulty. |
| Spec | 3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
\includegraphics{figure_9}
A block $B$ of weight $10 \text{N}$ lies at rest in equilibrium on a rough plane inclined at $\theta$ to the horizontal. A horizontal force of magnitude $2 \text{N}$, acting above a line of greatest slope, is applied to $B$ (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Complete the diagram in the Printed Answer Booklet to show all the forces acting on $B$. [1]
\end{enumerate}
It is given that $B$ remains at rest and the coefficient of friction between $B$ and the plane is 0.8.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the greatest possible value of $\tan \theta$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q9 [6]}}