| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Connected particles with friction |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem with friction requiring straightforward application of Newton's laws and friction formulae. Part (i) involves resolving forces and using F=μR in limiting equilibrium (routine 5-mark question). Part (ii) adds a horizontal force but uses the same principles. The problem requires no novel insight—just systematic application of standard mechanics techniques with clear force diagrams. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03r Friction: concept and vector form3.03u Static equilibrium: on rough surfaces |
\includegraphics{figure_3}
A block $B$ of mass $0.4$ kg and a particle $P$ of mass $0.3$ kg are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. $B$ is in contact with the table and the part of the string between $B$ and the pulley is horizontal. $P$ hangs freely below the pulley (see diagram).
\begin{enumerate}[label=(\roman*)]
\item The system is in limiting equilibrium with the string taut and $P$ on the point of moving downwards. Find the coefficient of friction between $B$ and the table. [5]
\item A horizontal force of magnitude $X$ N, acting directly away from the pulley, is now applied to $B$. The system is again in limiting equilibrium with the string taut, and with $P$ now on the point of moving upwards. Find the value of $X$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q3 [8]}}