| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Standard +0.3 This is a straightforward application of equilibrium conditions for forces and moments. Part (a) requires resolving forces to find F using the condition that forces sum to zero for a couple. Part (b) requires calculating moments about a point to find the couple. Both parts use standard Further Maths mechanics techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | F=ai+bj |
| a+2−3=0 and 2+1+b=0 | M1 | 1.1 |
| F=i−3j | A1 | 1.1 |
| F = 10 | A1ft | 1.1 |
| Direction is 71.6 below the horizontal | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | 3(2)+2(2)−2(1)−1(3) |
| e.g. taking moments about O: | M1 | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | A1 | 1.1 |
| anti-clockwise | A1 | 2.5 |
Question 3:
3 | (a) | F=ai+bj
a+2−3=0 and 2+1+b=0 | M1 | 1.1 | Setting up equations for a and b | Allow sign errors only
F=i−3j | A1 | 1.1
F = 10 | A1ft | 1.1 | oe e.g. 3.16 (ft their F) | 3.16227766…
Direction is 71.6 below the horizontal | A1 | 1.1 | oe 18.4 to the downward vertical | In radians: 1.25 or
0.322
[4]
3 | (b) | 3(2)+2(2)−2(1)−1(3)
e.g. taking moments about O: | M1 | 1.1a | Taking moments about any point with
correct number of terms
5 | A1 | 1.1
anti-clockwise | A1 | 2.5 | oe (could be seen on a diagram)
[3]The vertices of a triangular lamina, which is in the $x$–$y$ plane, are at the origin O and the points A$(2, 3)$ and B$(-2, 1)$.
Forces $2\mathbf{i} + \mathbf{j}$ and $-3\mathbf{i} + 2\mathbf{j}$ are applied to the lamina at A and B, respectively, and a force $\mathbf{F}$, whose line of action is in the $x$–$y$ plane, is applied at O.
The three forces form a couple.
\begin{enumerate}[label=(\alph*)]
\item Determine the magnitude and the direction of $\mathbf{F}$. [4]
\item Determine the magnitude and direction of the additional couple that must be applied to the lamina in order to keep it in equilibrium. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2020 Q3 [7]}}