| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question testing basic vector addition and trigonometry. Part (i) uses Pythagoras and inverse tan with perpendicular forces—standard textbook material. Part (ii) requires resolving forces perpendicular to the 8N force, but the setup is clearly guided by the diagram and the method is routine. No novel problem-solving or insight required, just direct application of well-practiced techniques. |
| Spec | 3.03a Force: vector nature and diagrams3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (iia)(iib) numbers must be \(+\)ve | For A marks | |
| (iib) \(R + 12\cos 41.8 = 0\) | M0 | |
| (iib) Squaring, adding and square rooting \(12\cos\theta\) and \((8 - 12\sin\theta)\) with candidate's value of \(\theta\) from (iia) | Valid method |
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| (iia)(iib) numbers must be $+$ve | | For A marks |
| (iib) $R + 12\cos 41.8 = 0$ | M0 | |
| (iib) Squaring, adding and square rooting $12\cos\theta$ and $(8 - 12\sin\theta)$ with candidate's value of $\theta$ from (iia) | | Valid method |
---3 Two forces of magnitudes 8 N and 12 N act at a point $O$.\\
(i) Given that the two forces are perpendicular to each other, find
\begin{enumerate}[label=(\alph*)]
\item the angle between the resultant and the 12 N force,
\item the magnitude of the resultant.\\
(ii) It is given instead that the resultant of the two forces has magnitude $R \mathrm {~N}$ and acts in a direction perpendicular to the 8 N force (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{b7f05d10-9d3c-4098-846d-ca6511c75c5d-2_248_388_1877_826}\\
(a) Calculate the angle between the resultant and the 12 N force.\\
(b) Find $R$.
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2013 Q3 [9]}}