| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Triangle of forces method |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem requiring either a triangle of forces diagram or resolving forces in two perpendicular directions. The methods are standard A-level techniques with minimal problem-solving required—students simply apply sine/cosine rules or component resolution to find two unknowns. While it's a Further Maths question, the mechanics content is routine and below average difficulty for A-level. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | e.g. |
| [1] | 1.1 | All three lengths and both angles must be correctly |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | (i) | sinθ sin40 |
| Answer | Marks |
|---|---|
| θ=21.5 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Correct application of sine rule (oe) for their closed |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | (ii) | P2 =42 +72 −2(4)(7)cos(180−40−θ) |
| P=9.57 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Correct application of cosine rule (oe) with their θ(or |
Question 1:
1 | (a) | e.g. | B1
[1] | 1.1 | All three lengths and both angles must be correctly
placed (arrows not required)
(b) | (i) | sinθ sin40
=
4 7
θ=21.5 | M1
A1
[2] | 1.1
1.1 | Correct application of sine rule (oe) for their closed
figure or resolving horizontally 7sinθ=4sin40
21.54964123…
(b) | (ii) | P2 =42 +72 −2(4)(7)cos(180−40−θ)
P=9.57 | M1
A1
[2] | 1.1
1.1 | Correct application of cosine rule (oe) with their θ(or
just θ) or correctly resolving vertically
P=4cos40+7cosθoe for example,
72 =42 +P2 −2(4)(P)cos40
sin(140−θ)
sin40
=
P 7
9.57487554… - accept 9.58 (from using 21.5 for θ)\includegraphics{figure_1}
Three forces of magnitudes 4 N, 7 N and $P$ N act at a point in the directions shown in the diagram.
The forces are in equilibrium.
\begin{enumerate}[label=(\alph*)]
\item Draw a closed figure to represent the three forces. [1]
\item Hence, or otherwise, find the following.
\begin{enumerate}[label=(\roman*)]
\item The value of $\theta$. [2]
\item The value of $P$. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2022 Q1 [5]}}