| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Standard +0.3 This is a standard M2 statics problem requiring moments about a point, resolution of forces, and friction inequality. The geometry is straightforward (given angle and heights), and the method is routine: take moments about P to find reaction at A, resolve forces to find normal reaction (shown to be 25N), then apply friction condition. While multi-step with 12 marks total, it follows a predictable template for equilibrium problems without requiring novel insight or complex geometry. |
| Spec | 3.03v Motion on rough surface: including inclined planes3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Moments about A: \(30 \times 1.5 \cos 15 = d \times N\) | M1 | Requires correct terms of correct structure. Condone with value of d not yet found. |
| \(30 \times 1.5 \cos 15 = \frac{0.45}{\sin 15} N\) | A2 | -1 each error. Requires a value for d. Accept unsimplified. \(d = 1.738\ldots\) |
| \(N = 100 \cos 15 \sin 15 = 25 \text{ (N)}\) | A1 | Watch out for given answer |
| (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Moments about P: \(R \times d \cos 15 = 30 \times (d - 1.5) \cos 15\) | M1 | Terms of correct structure. Condone sign errors & trig confusion. |
| A2ft | their d. Correct unsimplified. -1 each error | |
| \(R = \frac{30(d-1.5)}{d} = 4.118095\ldots\) | A1 | 4.1 or better |
| (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Resolving horizontally at P: \(N \cos 75 = F \cos 15\) | M1 | Condone trig confusion |
| A1 | ||
| \(F = \frac{N \cos 75}{\cos 15}\) | M1 | Use of \(F \leq \mu N\) |
| \(\mu \geq \frac{F}{N}; \quad \mu \geq \frac{\cos 75}{\cos 15}\) | ||
| \(\mu \geq 0.268\) | A1 | 0.27 or better |
| (4) | ||
| [12] |
**(a)**
| Moments about A: $30 \times 1.5 \cos 15 = d \times N$ | M1 | Requires correct terms of correct structure. Condone with value of d not yet found. |
| $30 \times 1.5 \cos 15 = \frac{0.45}{\sin 15} N$ | A2 | -1 each error. Requires a value for d. Accept unsimplified. $d = 1.738\ldots$ |
| $N = 100 \cos 15 \sin 15 = 25 \text{ (N)}$ | A1 | **Watch out for given answer** |
| | (4) | |
**(b)**
| Moments about P: $R \times d \cos 15 = 30 \times (d - 1.5) \cos 15$ | M1 | Terms of correct structure. Condone sign errors & trig confusion. |
| | A2ft | their d. Correct unsimplified. -1 each error |
| $R = \frac{30(d-1.5)}{d} = 4.118095\ldots$ | A1 | 4.1 or better |
| | (4) | |
**(c)**
| Resolving horizontally at P: $N \cos 75 = F \cos 15$ | M1 | Condone trig confusion |
| | A1 | |
| $F = \frac{N \cos 75}{\cos 15}$ | M1 | Use of $F \leq \mu N$ |
| $\mu \geq \frac{F}{N}; \quad \mu \geq \frac{\cos 75}{\cos 15}$ | | |
| $\mu \geq 0.268$ | A1 | 0.27 or better |
| | (4) |
| | [12] | |\includegraphics{figure_3}
A uniform rod $AB$ has weight 30 N and length 3 m. The rod rests in equilibrium on a rough horizontal peg $P$ with its end $A$ on smooth horizontal ground. The rod is in a vertical plane perpendicular to the peg. The rod is inclined at 15° to the ground and the point of contact between the peg and the rod is 45 cm above the ground, as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item Show that the normal reaction at $P$ has magnitude 25 N. [4]
\item Find the magnitude of the force on the rod at $A$. [4]
\end{enumerate}
The coefficient of friction between the rod and the peg is $\mu$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the range of possible values of $\mu$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q6 [12]}}