| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Moderate -0.3 This is a standard two-body pulley system problem requiring students to write Newton's second law equations for each mass and solve simultaneously. While it involves multiple steps (two equations, elimination, solving), the setup is completely routine for M1 with no conceptual surprises—slightly easier than average due to its textbook nature. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Block: \(T - 14.8 = 4a\) | B1 | |
| Sphere: \(2g - T = 2a\) | B1 | |
| Both equations required | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Adding: \(2g - 14.8 = 6a\) | M1 | |
| \(19.6 - 14.8 = 6a \Rightarrow a = 0.8\) m s\(^{-2}\) | A1 | |
| \(T = 14.8 + 4(0.8) = 18\) N | A1 |
# Question 5:
**(i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Block: $T - 14.8 = 4a$ | B1 | |
| Sphere: $2g - T = 2a$ | B1 | |
| Both equations required | B1 | |
**(ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Adding: $2g - 14.8 = 6a$ | M1 | |
| $19.6 - 14.8 = 6a \Rightarrow a = 0.8$ m s$^{-2}$ | A1 | |
| $T = 14.8 + 4(0.8) = 18$ N | A1 | |5 A block of mass 4 kg slides on a horizontal plane against a constant resistance of 14.8 N . A light, inextensible string is attached to the block and, after passing over a smooth pulley, is attached to a freely hanging sphere of mass 2 kg . The part of the string between the block and the pulley is horizontal. This situation is shown in Fig. 5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{52d6c914-b204-4587-a82e-fbab6693fcf8-3_250_671_1466_696}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
The tension in the string is $T \mathrm {~N}$ and the acceleration of the block and of the sphere is $a \mathrm {~ms} ^ { - 2 }$.\\
(i) Write down the equation of motion of the block and also the equation of motion of the sphere, each in terms of $T$ and $a$.\\
(ii) Find the values of $T$ and $a$.
\hfill \mbox{\textit{OCR MEI M1 2007 Q5 [6]}}