| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring systematic resolution of forces in two perpendicular directions and calculation of moments about a point. Part (a) is routine verification, part (b) applies standard moment formula with given perpendicular distances, and part (c) requires recognizing that zero resultant force with non-zero moment produces pure rotation. All techniques are standard A-level mechanics with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03p Resultant forces: using vectors3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total in the AB direction is \(3-3=0\); Total in the AD direction is \(4+5-9=0\); So zero resultant force | M1 | Considers forces in each direction |
| A1 | AG Allow if clear statement of zero force in two perpendicular directions. Do not allow for "equilibrium" on its own e.g. \(3=3\) and \(4+5=9\) is not sufficient without a comment | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Take moments anticlockwise (N cm) | B1 | At least one moment about the centre or any corner |
| \(4\times14-5\times14+3\times9-9\times14+3\times9\) | M1 | Combines moments of 5 forces about the centre. Allow only sign errors |
| \(=-86\text{ N cm}\) | Do not allow as final answer | |
| \(=-0.86\text{ [N m]}\) | A1 | Allow for \(0.86\) N m clockwise but not \(-0.86\) N m clockwise. Allow B1 SC1 for \(-0.86\) N m as the total moment about a different point |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The book will rotate | B1 | Allow turn or spin but not move, tilt or flip |
| clockwise [about the centre of mass] | B1 | Allow "there is a clockwise moment" for the second mark |
| [2] |
## Question 7:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total in the AB direction is $3-3=0$; Total in the AD direction is $4+5-9=0$; So zero resultant force | M1 | Considers forces in each direction |
| | A1 | AG Allow if clear statement of zero force in two perpendicular directions. Do not allow for "equilibrium" on its own e.g. $3=3$ and $4+5=9$ is not sufficient without a comment |
| [2] | | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Take moments anticlockwise (N cm) | B1 | At least one moment about the centre or any corner |
| $4\times14-5\times14+3\times9-9\times14+3\times9$ | M1 | Combines moments of 5 forces about the centre. Allow only sign errors |
| $=-86\text{ N cm}$ | | Do not allow as final answer |
| $=-0.86\text{ [N m]}$ | A1 | Allow for $0.86$ N m clockwise but not $-0.86$ N m clockwise. Allow B1 SC1 for $-0.86$ N m as the total moment about a different point |
| [3] | | |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| The book will rotate | B1 | Allow turn or spin but not move, tilt or flip |
| clockwise [about the centre of mass] | B1 | Allow "there is a clockwise moment" for the second mark |
| [2] | | |7 A rectangular book ABCD rests on a smooth horizontal table. The length of AB is 28 cm and the length of AD is 18 cm . The following five forces act on the book, as shown in the diagram.
\begin{itemize}
\item 4 N at A in the direction AD
\item 5 N at B in the direction BC
\item 3 N at B in the direction BA
\item 9 N at D in the direction DA
\item 3 N at D in the direction DC\\
\includegraphics[max width=\textwidth, alt={}, center]{1d0ca3d5-6529-435f-a0b8-50ea4859adde-06_663_830_774_242}
\begin{enumerate}[label=(\alph*)]
\item Show that the resultant of the forces acting on the book has zero magnitude.
\item Find the total moment of the forces about the centre of the book. Give your answer in Nm .
\item Describe how the book will move under the action of these forces.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2024 Q7 [7]}}