| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Two particles over single pulley |
| Difficulty | Moderate -0.3 This is a standard M1 connected particles problem with friction in limiting equilibrium. Part (i) requires straightforward application of equilibrium conditions (T = 0.3g, friction = μR = T) to find μ. Part (ii) adds a horizontal force but uses the same principles. The problem is slightly easier than average because it's a textbook setup with clear equilibrium conditions and no complex geometry or novel reasoning required. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03r Friction: concept and vector form3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(T = 0.3g\) \(F = T\) \(R = 0.4g\) Coefficient is 0.75 | B1 B1 B1 M1 A1 | At particle (or 0.3g -T= 0.3a) Or F = cv(T at particle) (or T - F = 0.4a) For using F = \(\mu\) R |
| (ii) \(X = 0.3g + 0.3g\) \(X = 5.88N\) | M1 A1ft A1 | For resolving 3 relevant forces on B horizontally, a=0 Ft cv(\(\mu\)) cv(R) |
(i) $T = 0.3g$ $F = T$ $R = 0.4g$ Coefficient is 0.75 | B1 B1 B1 M1 A1 | At particle (or 0.3g -T= 0.3a) Or F = cv(T at particle) (or T - F = 0.4a) For using F = $\mu$ R
(ii) $X = 0.3g + 0.3g$ $X = 5.88N$ | M1 A1ft A1 | For resolving 3 relevant forces on B horizontally, a=0 Ft cv($\mu$) cv(R)
---\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 2007 Q3 [8]}}