| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Limiting equilibrium both directions |
| Difficulty | Standard +0.8 This is a two-part limiting equilibrium problem requiring students to set up force equations in both directions (down and up the slope), then solve simultaneously to eliminate μ and find α. While the mechanics is standard A-level content, the algebraic manipulation across two cases and the need to recognize how to combine the equations elevates this above routine exercises. It requires systematic problem-solving rather than just applying a single formula. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
10 A body of mass 20 kg is on a rough plane inclined at angle $\alpha$ to the horizontal.\\
The body is held at rest on the plane by the action of a force of magnitude $P \mathrm {~N}$.\\
The force is acting up the plane in a direction parallel to a line of greatest slope of the plane.\\
The coefficient of friction between the body and the plane is $\mu$.
\begin{enumerate}[label=(\alph*)]
\item When $P = 100$, the body is on the point of sliding down the plane.
Show that $g \sin \alpha = g \mu \cos \alpha + 5$.
\item When $P$ is increased to 150, the body is on the point of sliding up the plane.
Use this, and your answer to part (a), to find an expression for $\alpha$ in terms of $g$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 Q10 [7]}}