| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with strut or direct force support |
| Difficulty | Standard +0.3 This is a straightforward M1 moments question requiring taking moments about the pivot, resolving forces, and stating a standard modelling assumption. The geometry is simple (30° and 60° angles give nice exact values), and the method is routine textbook application of equilibrium conditions. Slightly easier than average due to the standard setup and clean numbers. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Resolve: \(F \sin 60° = T \sin 30°\), \(F \cos 60° + T \cos 30° = 0.8g\) | M1 A1 A1 | |
| Hence \(F\sqrt{3} = T\), \(F + T\sqrt{3} = 1.6g\) | ||
| \(4F = 1.6g\) | ||
| \(F = 3.92\) N | M1 M1 A1 | |
| (b) \(T = 3.92\sqrt{3} = 6.79\) N | M1 A1 | |
| (c) Modelled clay as a particle | B1 | Total: 9 marks |
**(a)** Resolve: $F \sin 60° = T \sin 30°$, $F \cos 60° + T \cos 30° = 0.8g$ | M1 A1 A1 |
Hence $F\sqrt{3} = T$, $F + T\sqrt{3} = 1.6g$ | |
$4F = 1.6g$ | |
$F = 3.92$ N | M1 M1 A1 |
**(b)** $T = 3.92\sqrt{3} = 6.79$ N | M1 A1 |
**(c)** Modelled clay as a particle | B1 | **Total: 9 marks**3. A lump of clay, of mass 0.8 kg , is attached to the end $A$ of a light $\operatorname { rod } A B$, which is pivoted at its other end $B$ so that it can rotate smoothly in a vertical plane. A force is applied to $A$ at an angle of $60 ^ { \circ }$ to the vertical, as shown, the magnitude $F \mathrm {~N}$ of this force being just enough to hold the lump of clay in equilibrium with $A B$ inclined\\
\includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_309_335_1453_1590}\\
at an angle of $30 ^ { \circ }$ to the upward vertical.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $F$,
\item Find the magnitude of the force in the $\operatorname { rod } A B$.
\item State the modelling assumption that you have made about the lump of clay.\\
(6 marks)\\
(2 marks)\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [9]}}