| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod with string perpendicular |
| Difficulty | Standard +0.3 This is a standard M2 moments equilibrium problem requiring resolution of forces and taking moments about a point. Part (a) involves straightforward moment calculation about point A to find tension. Part (b) requires resolving horizontally and vertically, then using F=μR at limiting friction. While it has multiple steps (11 marks total), the techniques are routine for M2 students with no novel problem-solving required—slightly easier than average overall. |
| Spec | 3.03v Motion on rough surface: including inclined planes3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| Taking moments about A: | M1 |
| \(4g \times 0.7 \times \cos 20° = 1.4T\) | A1 A1 |
| \(T = 18.4\) N | A1 |
| Answer | Marks |
|---|---|
| \(\uparrow\) \(R + T\cos 20 = 4g\) | M1 |
| \(R = 4g - T\cos 20°\) | M1 A1 |
| \(\rightarrow\) \(F = T\sin 20\) | M1 A1 |
| \(F = \mu R \Rightarrow T\sin 20° = \mu(4g - T\cos 20°)\) | DM1 A1 |
| \(\mu = \frac{T\sin 20°}{4g - T\cos 20°} = 0.29\) | A1 |
## (a)
| Taking moments about A: | M1 |
| $4g \times 0.7 \times \cos 20° = 1.4T$ | A1 A1 |
| $T = 18.4$ N | A1 |
**Total: 4 marks**
## (b)
| $\uparrow$ $R + T\cos 20 = 4g$ | M1 |
| $R = 4g - T\cos 20°$ | M1 A1 |
| $\rightarrow$ $F = T\sin 20$ | M1 A1 |
| $F = \mu R \Rightarrow T\sin 20° = \mu(4g - T\cos 20°)$ | DM1 A1 |
| $\mu = \frac{T\sin 20°}{4g - T\cos 20°} = 0.29$ | A1 |
**Total: 7 marks**
**Question 5 Total: 11 marks**
---\includegraphics{figure_2}
A uniform rod $AB$ has mass $4$ kg and length $1.4$ m. The end $A$ is resting on rough horizontal ground. A light string $BC$ has one end attached to $B$ and the other end attached to a fixed point $C$. The string is perpendicular to the rod and lies in the same vertical plane as the rod. The rod is in equilibrium, inclined at $20°$ to the ground, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string.
[4]
\end{enumerate}
Given that the rod is about to slip,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the coefficient of friction between the rod and the ground.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2012 Q5 [11]}}