| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Ring on horizontal rod equilibrium |
| Difficulty | Moderate -0.8 This is a straightforward M1 equilibrium problem requiring resolution of forces in two perpendicular directions and application of F=μR at limiting equilibrium. The setup is standard with given numerical values, requiring only routine application of Newton's laws and friction formula with no conceptual challenges or multi-step reasoning. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\pm R + 1.2\sin 40° = 0.25g\) | M1 A1 | (4 marks) |
| Solving to \(R = 1.7\) (N) (accept 1.68) | DM1 A1 | |
| (b) \(F = 1.2\cos 40°\) (\(\approx 0.919\)) | M1 A1 | (6 marks) |
| Use of \(F = \mu R\) | B1 | |
| \(1.2\cos 40° = \mu R\) | DM1 A1ft | |
| \(\mu \approx 0.55\) (accept 0.548) | A1 cao | |
| [10] |
**(a)** $\pm R + 1.2\sin 40° = 0.25g$ | M1 A1 | (4 marks)
Solving to $R = 1.7$ (N) (accept 1.68) | DM1 A1 |
**(b)** $F = 1.2\cos 40°$ ($\approx 0.919$) | M1 A1 | (6 marks)
Use of $F = \mu R$ | B1 |
$1.2\cos 40° = \mu R$ | DM1 A1ft |
$\mu \approx 0.55$ (accept 0.548) | A1 cao |
| | [10] |5.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{5b5d70b1-1eb6-461f-9277-5912b914f443-08_218_479_287_744}
\end{center}
\end{figure}
A small ring of mass 0.25 kg is threaded on a fixed rough horizontal rod. The ring is pulled upwards by a light string which makes an angle $40 ^ { \circ }$ with the horizontal, as shown in Figure 3. The string and the rod are in the same vertical plane. The tension in the string is 1.2 N and the coefficient of friction between the ring and the rod is $\mu$. Given that the ring is in limiting equilibrium, find
\begin{enumerate}[label=(\alph*)]
\item the normal reaction between the ring and the rod,
\item the value of $\mu$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q5 [10]}}