| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough incline connected to particle on horizontal surface or other incline |
| Difficulty | Challenging +1.2 This is a connected particles problem with friction on both surfaces and a constraint relating the coefficients. Part (a) requires setting up force equations for both masses with the friction relationship, then solving simultaneously - a standard A-level mechanics technique but with multiple steps. Part (b) uses SUVAT after the string breaks to find P's deceleration, then applies this to find B's deceleration - straightforward application once the setup is understood. The 60° angle and friction relationship add computational complexity but no novel insight is required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
\includegraphics{figure_13}
The diagram shows a small block $B$, of mass $2 \text{kg}$, and a particle $P$, of mass $4 \text{kg}$, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane. The particle can move on the inclined plane, which is rough, and which makes an angle of $60°$ with the horizontal. The block can move on the horizontal surface, which is also rough.
The system is released from rest, and in the subsequent motion $P$ moves down the plane and $B$ does not reach the pulley.
It is given that the coefficient of friction between $P$ and the inclined plane is twice the coefficient of friction between $B$ and the horizontal surface.
\begin{enumerate}[label=(\alph*)]
\item Determine, in terms of $g$, the tension in the string. [7]
\end{enumerate}
When $P$ is moving at $2 \text{ms}^{-1}$ the string breaks. In the $0.5$ seconds after the string breaks $P$ moves $1.9 \text{m}$ down the plane.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the deceleration of $B$ after the string breaks. Give your answer correct to 3 significant figures. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q13 [12]}}