| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on smooth horizontal surface, particle hanging |
| Difficulty | Moderate -0.8 This is a standard introductory pulley system question requiring basic force diagrams and Newton's second law applications. Part (a) tests force identification, (b) requires simple equilibrium (T = 1.2g), (c) is given structure, and (d) involves solving two simultaneous equations. All steps are routine textbook exercises with no problem-solving insight needed, making it easier than average A-level questions. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Diagram: \(R\) (up), \(3g\) N (down), \(T\) (right), \(F\) (left) on block; \(T\) (up), \(1.2g\) N (down) on sphere | B1 | 3.3 — Both forces on the sphere correct and labelled |
| B1 | 3.3 — All forces correct on the block. Tension must be marked the same or if \(T_1\) and \(T_2\) used, equated to each other elsewhere. Horizontal force \(F\) must be in correct direction |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| For equilibrium: sphere gives \(T = 1.2g\) N | M1 | 1.1b — soi |
| For block: \(F = T = 1.2g = 11.76\) | A1 | 1.1b — any form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(1.2g - T = 1.2a\) | B1 | 3.4 — cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| For block \(T = 3a\); add equations: \(1.2g = 4.2a\) | M1 | 1.1a — Attempt to solve simultaneous equations leading to value for \(a\). Do not award if equation 11(c) does not have \(T\) |
| \(a = 2.8 \text{ ms}^{-2}\); substitute \(T = 3a = 8.4\) | A1 | 1.1b — Cao. Allow \(\dfrac{6}{7}g\) |
## Question 11(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Diagram: $R$ (up), $3g$ N (down), $T$ (right), $F$ (left) on block; $T$ (up), $1.2g$ N (down) on sphere | B1 | 3.3 — Both forces on the sphere correct and labelled |
| | B1 | 3.3 — All forces correct on the block. Tension must be marked the same or if $T_1$ and $T_2$ used, equated to each other elsewhere. Horizontal force $F$ must be in correct direction |
**Total: [2]**
---
## Question 11(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| For equilibrium: sphere gives $T = 1.2g$ N | M1 | 1.1b — soi |
| For block: $F = T = 1.2g = 11.76$ | A1 | 1.1b — any form |
**Total: [2]**
---
## Question 11(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $1.2g - T = 1.2a$ | B1 | 3.4 — cao |
**Total: [1]**
---
## Question 11(d):
| Answer/Working | Mark | Guidance |
|---|---|---|
| For block $T = 3a$; add equations: $1.2g = 4.2a$ | M1 | 1.1a — Attempt to solve simultaneous equations leading to value for $a$. Do not award if equation 11(c) does not have $T$ |
| $a = 2.8 \text{ ms}^{-2}$; substitute $T = 3a = 8.4$ | A1 | 1.1b — Cao. Allow $\dfrac{6}{7}g$ |
**Total: [2]**
---11 A block of mass 3 kg is at rest on a smooth horizontal table. It is attached to a light inextensible string which passes over a smooth pulley. This part of the string is horizontal. A sphere of mass 1.2 kg is attached to the other end of the string. The sphere hangs with this part of the string vertical as shown in the diagram. A horizontal force of magnitude $F$ N is applied to the block to prevent motion.\\
\includegraphics[max width=\textwidth, alt={}, center]{1d1e41f3-a834-4230-b6e1-4b0be9450d30-7_268_718_493_244}
\begin{enumerate}[label=(\alph*)]
\item Complete the copy of the diagram in the Printed Answer Booklet to show all the forces acting on the block and the sphere.
\item Find the value of $F$.
The force $F$ N is removed, and the system begins to move.
\item The equation of motion of the block is $\mathrm { T } = 3 \mathrm { a }$, where $T \mathrm {~N}$ is the tension in the string and $a \mathrm {~ms} ^ { - 2 }$ is the acceleration of the block.
Write down the equation of motion of the sphere.
\item Find the value of $T$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2023 Q11 [7]}}