| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Moderate -0.3 This is a straightforward mechanics question testing basic understanding of couples and resultant forces. Part (a) requires adding forces to create couples of specified magnitudes using given diagrams, which is routine application of the couple formula (force × perpendicular distance). Part (b) involves resolving forces to find an unknown force magnitude and then calculating the resulting couple - standard techniques with no novel problem-solving required. The question is slightly easier than average due to its direct application of formulas and clear setup. |
| Spec | 3.03a Force: vector nature and diagrams3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | 4 N |
| 4 N | B1 |
| Answer | Marks |
|---|---|
| B1 | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Consider six features: |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | (i) | T = 5 2 + 3 2 = 3 4 ( = 5 .8 3 0 9 5 ) |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | Taking moments about A: 34−52 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 Nm | A1 | 1.1 |
| Clockwise | B1 | 1.1 |
Question 1:
1 | (a) | 4 N
4 N | B1
B1
B1 | 1.1
1.1
1.1 | Consider six features:
Magnitude, direction and position
of each force
Magnitudes taken as labelled
(regardless of length) or inferred
from length if not labelled
Give B3 for all 6 features correct
Give B2 for any 4 features correct
Give B1 for any 2 features correct
If more than one additional force
shown, no features can be scored
for that part.
4 N
1 N
5 N
[3]
(b) | (i) | T = 5 2 + 3 2 = 3 4 ( = 5 .8 3 0 9 5 ) | B1 | 1.1 | Accept exact or rounded forms.
[1]
(ii) | Taking moments about A: 34−52 | M1 | 1.1 | (±) 3d ± 5d (± …)
1 2
Or other clear attempt to calculate
moment
2 Nm | A1 | 1.1 | Allow ˗2
Clockwise | B1 | 1.1 | Independent
M1A1B0 for ˗2 Nm anticlockwise
B0 for ‘To the right’ etc
[3]1
\begin{enumerate}[label=(\alph*)]
\item Fig. 1.1 and Fig. 1.2 show rigid rods with forces acting as marked. The diagrams are to scale, and in each figure the side length of a grid square is 1 metre.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d1ec7861-dc8b-450b-8e05-c70479ab0dc2-2_428_552_443_319}
\captionsetup{labelformat=empty}
\caption{Fig. 1.1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d1ec7861-dc8b-450b-8e05-c70479ab0dc2-2_431_553_440_1005}
\captionsetup{labelformat=empty}
\caption{Fig. 1.2}
\end{center}
\end{figure}
\begin{itemize}
\item On the copy of Fig. 1.1 in the Printed Answer Booklet, add, to scale, a force so that the overall system represents an anti-clockwise couple of magnitude 24 Nm .
\item On the copy of Fig. 1.2 in the Printed Answer Booklet, add, to scale, a force so that the overall system represents a clockwise couple of magnitude 1 Nm .
\item Fig. 1.3 shows a rectangular lamina with two coplanar forces acting as marked. Each grid square has side length 1 m .
\end{itemize}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d1ec7861-dc8b-450b-8e05-c70479ab0dc2-2_561_761_1452_315}
\captionsetup{labelformat=empty}
\caption{Fig. 1.3}
\end{center}
\end{figure}
A third coplanar force, of magnitude $T \mathrm {~N}$, acts at A so that the resultant force on the lamina is zero.
\begin{enumerate}[label=(\roman*)]
\item Calculate the value of $T$.
\item Determine the magnitude and direction of the couple represented by this system of three forces.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS 2022 Q1 [7]}}