| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Particle suspended by strings |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem with friction and moments. Part (a) requires resolving forces on ring C (straightforward vertical equilibrium). Part (b) involves resolving horizontally and vertically on rings A or B, then applying friction law F=μR. The geometry is given (tan θ = 3/4), so students just need to find sin θ and cos θ, then systematically apply equilibrium conditions. While it requires multiple steps and careful bookkeeping across 10 marks total, it follows a predictable template for M1 statics problems with no novel insight required. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
## Part (a)
**Answer/Working:**
- For $C$: $27 \sin \theta = 3mg$
- $\sin \theta = \frac{3}{5} \Rightarrow T = \frac{5}{3}mg$ (*)
**Marks:** M1, A1, A1 (3 marks)
---
## Part (b)
**Answer/Working:**
- For $A$ or $B$: $R \uparrow = 2mg + T \sin \theta = 2mg + \frac{5}{3}mg \cdot \frac{3}{5} = \frac{7}{3}mg$
- $R \rightarrow$ for $A$ or $B$: $T \cos \theta = \mu R$
- Solve to get $\mu$ as number: $\frac{5}{3}mg \cdot \frac{4}{5} = \mu \cdot \frac{7}{3}mg \Rightarrow \mu = \frac{4}{7}$ (Accept 0.57 awrt)
**Marks:** M1, A1, M1, A1, M1, A1 (7 marks)
---\includegraphics{figure_2}
Two small rings, $A$ and $B$, each of mass $2m$, are threaded on a rough horizontal pole. The coefficient of friction between each ring and the pole is $\mu$. The rings are attached to the ends of a light inextensible string. A smooth ring $C$, of mass $3m$, is threaded on the string and hangs in equilibrium below the pole. The rings $A$ and $B$ are in limiting equilibrium on the pole, with $\angle BAC = \angle ABC = \theta$, where $\tan \theta = \frac{3}{4}$, as shown in Fig. 2.
\begin{enumerate}[label=(\alph*)]
\item Show that the tension in the string is $\frac{5}{2}mg$. [3]
\item Find the value of $\mu$. [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q4 [10]}}