| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Applied force in addition to weights |
| Difficulty | Standard +0.3 This is a straightforward two-body mechanics problem requiring Newton's second law applied to a system and individual bodies. Students must consider two cases (acceleration left vs right) and solve linear equations, but the method is standard and well-practiced in M1 courses with no conceptual surprises. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| System acceleration \(= 2\) m s\(^{-2}\); net force on system \(= (4+6)\times 2 = 20\) N | M1 | |
| \(30 - F = 20\) or \(F - 30 = 20\) (two cases) | M1 A1 | |
| \(F = 10\) N or \(F = 50\) N | A1 | Both values required |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Case \(F=10\): acceleration is to the right. For 6 kg block: \(30 - T = 6 \times 2 \Rightarrow T = 18\) N | M1 A1 | |
| Case \(F=50\): acceleration is to the left. For 6 kg block: \(T - 30 = 6 \times 2 \Rightarrow T = 42\) N | A1 |
# Question 5:
## Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| System acceleration $= 2$ m s$^{-2}$; net force on system $= (4+6)\times 2 = 20$ N | M1 | |
| $30 - F = 20$ or $F - 30 = 20$ (two cases) | M1 A1 | |
| $F = 10$ N or $F = 50$ N | A1 | Both values required |
## Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Case $F=10$: acceleration is to the right. For 6 kg block: $30 - T = 6 \times 2 \Rightarrow T = 18$ N | M1 A1 | |
| Case $F=50$: acceleration is to the left. For 6 kg block: $T - 30 = 6 \times 2 \Rightarrow T = 42$ N | A1 | |
---5 Fig. 5 shows blocks of mass 4 kg and 6 kg on a smooth horizontal table. They are connected by a light, inextensible string. As shown, a horizontal force $F \mathrm {~N}$ acts on the 4 kg block and a horizontal force of 30 N acts on the 6 kg block.
The magnitude of the acceleration of the system is $2 \mathrm {~ms} ^ { - 2 }$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{83e69140-4abf-4713-85da-922ce7530e47-3_106_1107_1708_479}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
(i) Find the two possible values of $F$.\\
(ii) Find the tension in the string in each case.
\hfill \mbox{\textit{OCR MEI M1 2013 Q5 [7]}}