| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with string support |
| Difficulty | Standard +0.3 This is a standard M2 moments problem requiring taking moments about the hinge, resolving forces, and finding resultant reaction. The setup is straightforward with clearly defined geometry (20° angle, horizontal force), and follows a routine method: moments equation for F, then resolution for reaction components. Slightly easier than average due to simple geometry and standard technique application. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) mom. about A: \(8g(\cos 20°) - F(2\sin 20°) = 0\) | M1 A1 | |
| \(F = \frac{4g}{\tan 20°} = 108\) N (3sf) | M1 A1 | |
| (b) resolve \(\rightarrow\): \(F + X = 0 \therefore X = 108\) | A1 | |
| resolve \(\uparrow\): \(Y - 8g = 0 \therefore Y = 78.4\) N | A1 | |
| mag. of reaction at hinge = \(\sqrt{(108)^2 + (78.4)^2} = 133\) N (3sf) | M1 A1 | |
| req'd angle = \(\tan^{-1}\frac{108}{78.4} = 54°\) (nearest degree) to the vertical | M1 A1 | (10) |
**(a)** mom. about A: $8g(\cos 20°) - F(2\sin 20°) = 0$ | M1 A1 |
$F = \frac{4g}{\tan 20°} = 108$ N (3sf) | M1 A1 |
**(b)** resolve $\rightarrow$: $F + X = 0 \therefore X = 108$ | A1 |
resolve $\uparrow$: $Y - 8g = 0 \therefore Y = 78.4$ N | A1 |
mag. of reaction at hinge = $\sqrt{(108)^2 + (78.4)^2} = 133$ N (3sf) | M1 A1 |
req'd angle = $\tan^{-1}\frac{108}{78.4} = 54°$ (nearest degree) to the vertical | M1 A1 | (10)5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{086ace58-0aa9-4f36-95c3-5698d14f511e-3_417_851_778_614}
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\caption{Fig. 2}
\end{center}
\end{figure}
A uniform rod $A B$ of length $2 a$ and mass 8 kg is smoothly hinged to a vertical wall at $A$.
The rod is held in equilibrium inclined at an angle of $20 ^ { \circ }$ to the horizontal by a force of magnitude $F$ newtons acting horizontally at $B$ which is below the level of $A$ as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Find, correct to 3 significant figures, the value of $F$.
\item Show that the magnitude of the reaction at the hinge is 133 N , correct to 3 significant figures, and find to the nearest degree the acute angle which the reaction makes with the vertical.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [10]}}