| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| 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 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 = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(P = 8\sqrt{2}\sin 45° + 12\sin 30°\) | M1 | Considering equilibrium in the vertical direction |
| M1 | Resolution of forces of 12 N and \(8\sqrt{2}\) N in the vertical direction. Do not allow sin-cos interchange for the 30° angle. | |
| \(P = 14\) | A1 | Dependent on both M marks |
| \(Q + 8\sqrt{2}\cos 45° = 12\cos 30°\) | B1 | |
| \(Q = 2.39\) | B1 |
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| $P = 8\sqrt{2}\sin 45° + 12\sin 30°$ | M1 | Considering equilibrium in the vertical direction |
| | M1 | Resolution of forces of 12 N and $8\sqrt{2}$ N in the vertical direction. Do not allow sin-cos interchange for the 30° angle. |
| $P = 14$ | A1 | Dependent on both M marks |
| $Q + 8\sqrt{2}\cos 45° = 12\cos 30°$ | B1 | |
| $Q = 2.39$ | B1 | |
---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]{f87e062a-fdf2-45cf-8bc0-d05683b28e1a-2_401_645_397_719}
\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 2015 Q1 [5]}}