| 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 simultaneous equations, which are standard M1 techniques with no novel problem-solving required. The 'show that' part provides scaffolding, making it easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 0 |
# Question 1
**M1** – Considering equilibrium in the vertical direction
**M1** – Resolution of forces of 12 N and $8\sqrt{2}$ N in the vertical direction
$P = 8\sqrt{2}\sin 45° + 12\sin 30°$
$P = 14$
**A1** – Do not allow sin-cos interchange for the $30°$ angle
$Q + 8\sqrt{2}\cos 45° = 12\cos 30°$
$Q = 2.39$
**B1** – Dependent on both M marks
**B1**
[5]1 Fig. 1 shows four forces acting at a point. The forces are in equilibrium.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{82f933a6-c17e-4b41-ae2b-3cc9d0ba975c-1_399_645_441_754}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Show that $P = 14$.\\
Find $Q$, giving your answer correct to 3 significant figures.
\hfill \mbox{\textit{OCR MEI M1 Q1 [5]}}