| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough incline, particle hanging |
| Difficulty | Standard +0.3 This is a standard A-level mechanics pulley problem requiring force diagrams, resolving forces on an incline with friction, and solving simultaneous equations. While it involves multiple components (friction, incline, connected particles), the setup is conventional and the solution method is routine for students who have practiced this topic. Slightly above average difficulty due to the multi-step nature and friction calculation, but no novel insight required. |
| Spec | 3.03l Newton's third law: extend to situations requiring force resolution3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Tension \(T\) on sphere and block (matching) | B1 | 1.1b |
| Normal reaction \(R\) | B1 | 1.1b |
| Friction \(F\) in correct direction and labelled | B1 | 1.1b |
| Both weights \(8g\) N and \(5g\) N correct | B1 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Sphere (downwards positive): \(5g - T = 5a\) | M1 | 1.1a |
| A1 | 1.1b | All correct — accept \(49 - T = 5a\), any form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(R = 8g\cos 15°\) | B1 | 3.1b |
| \(F = 0.3R = 2.4g\cos 15°\) | M1 | 3.4 |
| Newton's second law for block: \(T - 8g\sin 15° - F = 8a\) | M1 | 1.1a |
| A1 | 1.1b | All correct, FT their \(F\) |
| Add equations of motion (attempt to eliminate \(T\)) | M1 | 1.1a |
| \(5g - 8g\sin 15° - 2.4g\cos 15° = 13a\) | ||
| \(a = 0.461\) | A1 | 1.1b |
## Question 13(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Tension $T$ on sphere and block (matching) | B1 | 1.1b | Matching tensions on sphere and block (may also include tensions on pulley) |
| Normal reaction $R$ | B1 | 1.1b | Allow without label or $8g\cos 15°$ used |
| Friction $F$ in correct direction and labelled | B1 | 1.1b | This could be $0.3 \times 8g\cos 15°$ oe |
| Both weights $8g$ N and $5g$ N correct | B1 | 1.1b | Do not award if weight and its components shown together (unless dotted or similar) or any other extra forces |
**Total: [4]**
## Question 13(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Sphere (downwards positive): $5g - T = 5a$ | M1 | 1.1a | Newton's second law, allow sign errors |
| | A1 | 1.1b | All correct — accept $49 - T = 5a$, any form |
**Total: [2]**
## Question 13(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $R = 8g\cos 15°$ | B1 | 3.1b | |
| $F = 0.3R = 2.4g\cos 15°$ | M1 | 3.4 | FT their $R$ |
| Newton's second law for block: $T - 8g\sin 15° - F = 8a$ | M1 | 1.1a | Allow one missing or incorrect force, must be dimensionally correct. FT their $F$ |
| | A1 | 1.1b | All correct, FT their $F$ |
| Add equations of motion (attempt to eliminate $T$) | M1 | 1.1a | Attempt to eliminate $T$ |
| $5g - 8g\sin 15° - 2.4g\cos 15° = 13a$ | | | This equation with one missing or incorrect force implies the previous M1A0M1 |
| $a = 0.461$ | A1 | 1.1b | |
**Total: [6]**
---13 A block of mass 8 kg is placed on a rough plane inclined at $15 ^ { \circ }$ to the horizontal. The coefficient of friction between the block and the plane is 0.3 .
One end of a light rope is attached to the block. The rope passes over a smooth pulley fixed at the top of the plane, and a sphere of mass 5 kg , attached to the other end of the rope, hangs vertically below the pulley. The part of the rope between the block and the pulley is parallel to the plane. The system is released from rest, and as the sphere falls the block moves directly up the plane with acceleration $a \mathrm {~ms} ^ { - 2 }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{8eeff88d-8b05-43c6-86a5-bd82221c0bea-08_252_803_1560_246}
\begin{enumerate}[label=(\alph*)]
\item On the diagram in the Printed Answer Booklet, show all the forces acting on the block and on the sphere.
\item Write down the equation of motion for the sphere.
\item Determine the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2023 Q13 [12]}}