| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| 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 apply standard techniques (resolving horizontally and vertically) with simple trigonometry to find two unknowns. It's more routine than average A-level questions since it's a direct application of a single method with no problem-solving insight required. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Resolving vertically: \(120 - Q - P\sin60° = 0\) | M1 | Attempt to resolve vertically |
| Resolving horizontally: \(40 - P\cos60° = 0\) | M1 | Attempt to resolve horizontally |
| \(P\cos60° = 40 \Rightarrow P = 80\) N | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(Q = 120 - 80\sin60°\) | M1 | Substituting their \(P\) |
| \(Q = 120 - 40\sqrt{3} \approx 50.7\) N | A1 | ft their \(P\) |
# Question 1:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resolving vertically: $120 - Q - P\sin60° = 0$ | M1 | Attempt to resolve vertically |
| Resolving horizontally: $40 - P\cos60° = 0$ | M1 | Attempt to resolve horizontally |
| $P\cos60° = 40 \Rightarrow P = 80$ N | A1 | cao |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $Q = 120 - 80\sin60°$ | M1 | Substituting their $P$ |
| $Q = 120 - 40\sqrt{3} \approx 50.7$ N | A1 | ft their $P$ |
---1 Fig. 1 shows four forces in equilibrium.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3be85526-3872-42ac-8278-1d4a3cf75ff7-2_369_332_413_868}
\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 2007 Q1 [5]}}