| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Equilibrium of particle under coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem requiring resolution of forces in two perpendicular directions. Students need to apply basic trigonometry and solve two simultaneous equations, which is a standard M1 technique with no novel problem-solving required. The question is slightly easier than average due to its routine nature and clear structure. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\rightarrow\quad 40 - P\cos60 = 0\) | M1 | For any resolution in an equation involving \(P\). Allow for \(P = 40\cos60\) or \(P = 40\cos30\) or \(P = 40\sin60\) or \(P = 40\sin30\) |
| A1 | Correct equation | |
| \(P = 80\) | A1 | cao |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\downarrow\quad Q + P\cos30 = 120\) | M1 | Resolve vert. All forces present. Allow \(\sin \leftrightarrow \cos\). No extra forces. Allow wrong signs |
| \(Q = 40(3 - \sqrt{3}) = 50.7179\ldots\) so \(50.7\) (3 s.f.) | A1 | cao |
| Total: 2 |
## Question 6:
**Part (i):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\rightarrow\quad 40 - P\cos60 = 0$ | M1 | For any resolution in an equation involving $P$. Allow for $P = 40\cos60$ or $P = 40\cos30$ or $P = 40\sin60$ or $P = 40\sin30$ |
| | A1 | Correct equation |
| $P = 80$ | A1 | cao |
| **Total: 3** | | |
**Part (ii):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\downarrow\quad Q + P\cos30 = 120$ | M1 | Resolve vert. All forces present. Allow $\sin \leftrightarrow \cos$. No extra forces. Allow wrong signs |
| $Q = 40(3 - \sqrt{3}) = 50.7179\ldots$ so $50.7$ (3 s.f.) | A1 | cao |
| **Total: 2** | | |
---6 Fig. 1 shows four forces in equilibrium.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{82f933a6-c17e-4b41-ae2b-3cc9d0ba975c-4_364_328_1748_901}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
(i) Find the value of $P$.\\
(ii) Hence find the value of $Q$.
\hfill \mbox{\textit{OCR MEI M1 Q6 [5]}}