| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Ring on vertical rod equilibrium |
| Difficulty | Standard +0.8 This is a multi-part statics problem requiring resolution of forces in two directions at ring A (with friction in limiting equilibrium), force resolution at point P, and analysis of ring B. It involves non-standard angles (given as decimals rather than exact values), friction calculations, and careful geometric reasoning about string tensions. The three-part structure with 12 total marks and the need to coordinate multiple equilibrium conditions makes this moderately challenging, though the techniques are standard M1 content. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
\includegraphics{figure_5}
Two small rings $A$ and $B$ are attached to opposite ends of a light inextensible string. The rings are threaded on a rough wire which is fixed vertically. $A$ is above $B$. A horizontal force is applied to a point $P$ of the string. Both parts $AP$ and $BP$ of the string are taut. The system is in equilibrium with angle $BAP = \alpha$ and angle $ABP = \beta$ (see diagram). The weight of $A$ is $2$ N and the tensions in the parts $AP$ and $BP$ of the string are $7$ N and $T$ N respectively. It is given that $\cos \alpha = 0.28$ and $\sin \alpha = 0.96$, and that $A$ is in limiting equilibrium.
\begin{enumerate}[label=(\roman*)]
\item Find the coefficient of friction between the wire and the ring $A$. [7]
\item By considering the forces acting at $P$, show that $T \cos \beta = 1.96$. [2]
\item Given that there is no frictional force acting on $B$, find the mass of $B$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q5 [12]}}