| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Range of equilibrium positions |
| Difficulty | Standard +0.3 This is a straightforward moments problem requiring students to apply equilibrium conditions (taking moments about two pivot points to find limiting positions). The setup is clear, the method is standard textbook material, and the arithmetic is manageable. Slightly easier than average due to its routine nature and clear structure. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Let reactions of supports on shelf be \(U\) N at C and \(V\) N at D; neither \(U\) nor \(V\) can be negative if shelf does not tip | M1 | May be implied |
| Any position between C and D must give \(U > 0\) and \(V > 0\) | B1 | Need not show but must be stated |
| Consider load between A and C, \(x\) cm from C; cw moments about C: if \(V \geq 0\) then \(W \times 60 \geq 3W \times x\) | M1 | moments about C |
| so \(x \leq 20\) | A1 | allow \(<\) |
| Consider load between D and B, \(y\) cm from D; anti-cw moments about D: if \(U \geq 0\) then \(W \times 30 \geq 3W \times y\) | B1 | allow \(<\) |
| so \(y \leq 10\) | ||
| The load must be placed not closer than 10 cm to A and 50 cm to B oe | A1 | Must be clear statement and include CD |
| [6] |
| Answer | Marks | Guidance |
|---|---|---|
| Question | AO1 | AO2 |
| 1 | 1 | |
| 2 | 3 | |
| 3 | 3 | 1 |
| 4a | 3 | |
| 4b | 3 | |
| ... | ... | ... |
| Totals | 50 | 21 |
## Question 15:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Let reactions of supports on shelf be $U$ N at C and $V$ N at D; neither $U$ nor $V$ can be negative if shelf does not tip | M1 | May be implied |
| Any position between C and D must give $U > 0$ and $V > 0$ | B1 | Need not show but must be stated |
| Consider load between A and C, $x$ cm from C; cw moments about C: if $V \geq 0$ then $W \times 60 \geq 3W \times x$ | M1 | moments about C |
| so $x \leq 20$ | A1 | allow $<$ |
| Consider load between D and B, $y$ cm from D; anti-cw moments about D: if $U \geq 0$ then $W \times 30 \geq 3W \times y$ | B1 | allow $<$ |
| so $y \leq 10$ | | |
| The load must be placed not closer than 10 cm to A and 50 cm to B oe | A1 | Must be clear statement and include CD |
| **[6]** | | |
I can see that the images provided only show the **mark allocation summary table** (page 17) and **blank pages** (pages 18-20). The actual mark scheme content (answers, working, guidance notes) for each question is not visible in these images — only the AO1/AO2/AO3 mark distribution totals are shown.
From what is visible, here is the mark allocation summary:
| Question | AO1 | AO2 | AO3(PS) | AO3(M) | Total |
|----------|-----|-----|---------|--------|-------|
| 1 | 1 | | 1 | | 2 |
| 2 | 3 | | | | 3 |
| 3 | 3 | 1 | | | 4 |
| 4a | 3 | | | | 3 |
| 4b | 3 | | | | 3 |
| ... | ... | ... | ... | ... | ... |
| **Totals** | **50** | **21** | **11** | **18** | **100** |
To provide the full mark scheme content (model answers, mark types, guidance), I would need the earlier pages of the document that contain the actual marking criteria for each question. Could you share those pages?15 Fig. 15 shows a uniform shelf AB of weight $W \mathrm {~N}$.\\
The shelf is 180 cm long and rests on supports at points C and D . Point C is 30 cm from A and point D is 60 cm from B .\\
side view
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ff44367e-c992-4e79-b255-5a04e0b8e21e-11_284_1169_1987_383}
\captionsetup{labelformat=empty}
\caption{Fig. 15}
\end{center}
\end{figure}
Determine the range of positions a point load of $3 W$ could be placed on the shelf without the shelf tipping.
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\hfill \mbox{\textit{OCR MEI Paper 1 Q15 [6]}}