| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Standard +0.3 This is a connected particles problem with friction, requiring standard applications of Newton's second law and friction inequalities. Part (a) is straightforward F=ma with given tension. Part (b) requires resolving forces on P to find friction coefficient. Part (c) needs careful consideration of forces on B to find limiting equilibrium condition. All steps are methodical applications of standard mechanics techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
\includegraphics{figure_10}
A rectangular block $B$ is at rest on a horizontal surface. A particle $P$ of mass 2.5 kg is placed on the upper surface of $B$. The particle $P$ is attached to one end of a light inextensible string which passes over a smooth fixed pulley. A particle $Q$ of mass 3 kg is attached to the other end of the string and hangs freely below the pulley. The part of the string between $P$ and the pulley is horizontal (see diagram).
The particles are released from rest with the string taut. It is given that $B$ remains in equilibrium while $P$ moves on the upper surface of $B$. The tension in the string while $P$ moves on $B$ is 16.8 N.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of $Q$ while $P$ and $B$ are in contact. [2]
\item Determine the coefficient of friction between $P$ and $B$. [3]
\item Given that the coefficient of friction between $B$ and the horizontal surface is $\frac{5}{49}$, determine the least possible value for the mass of $B$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2022 Q10 [8]}}