| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 12 |
| 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 horizontally and vertically, and finding resultant force magnitude/direction. The setup is straightforward with clear geometry (60° angle, midpoint attachment), and part (a) guides students by giving the answer to show. While it requires multiple steps and careful handling of distances and angles, it follows a well-practiced procedure with no novel insight needed, making it slightly easier than average. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | Mom. about \(A\): \(2ga + 6g(2a) - Ta\cos 60° = 0\); \(14ga = \frac{1}{2}Ta\) \(\therefore T = 28g\) | M1 A1, M1 A1 |
| (b) | Resolve \(\uparrow\): \(Y + T\cos 60° - 8g = 0\) \(\therefore Y = -6g\) | M1 A1 |
| Resolve \(\rightarrow\): \(X - T\sin 60° = 0\) \(\therefore X = 14\sqrt{3}g\) | M1 A1 | |
| Mag. of force at hinge: \(\sqrt{(14\sqrt{3}g)^2 + (-6g)^2} = 245\text{ N}\) (3sf) | M1 A1 | |
| Req'd angle \(= \tan^{-1}\frac{-6g}{14\sqrt{3}g} = 13.9°\) (3sf) below horizontal (away from wall) | M1 A1 | (12 marks total) |
(a) | Mom. about $A$: $2ga + 6g(2a) - Ta\cos 60° = 0$; $14ga = \frac{1}{2}Ta$ $\therefore T = 28g$ | M1 A1, M1 A1 |
(b) | Resolve $\uparrow$: $Y + T\cos 60° - 8g = 0$ $\therefore Y = -6g$ | M1 A1 |
| Resolve $\rightarrow$: $X - T\sin 60° = 0$ $\therefore X = 14\sqrt{3}g$ | M1 A1 |
| Mag. of force at hinge: $\sqrt{(14\sqrt{3}g)^2 + (-6g)^2} = 245\text{ N}$ (3sf) | M1 A1 |
| Req'd angle $= \tan^{-1}\frac{-6g}{14\sqrt{3}g} = 13.9°$ (3sf) below horizontal (away from wall) | M1 A1 | (12 marks total)
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{f5449ec3-ead0-464f-9d03-f225cd21bca6-3_390_725_191_575}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Figure 1 shows a uniform rod $A B$ of mass 2 kg and length $2 a$. The end $A$ is attached by a smooth hinge to a fixed point on a vertical wall so that the rod can rotate freely in a vertical plane. A mass of 6 kg is placed at $B$ and the rod is held in a horizontal position by a light string joining the midpoint of the rod to a point $C$ on the wall, vertically above $A$. The string is inclined at an angle of $60 ^ { \circ }$ to the wall.
\begin{enumerate}[label=(\alph*)]
\item Show that the tension in the string is $28 g$.
\item Find the magnitude and direction of the force exerted by the hinge on the rod, giving your answers correct to 3 significant figures.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [12]}}