| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | String breaks during motion |
| Difficulty | Standard +0.3 This is a standard M1 pulley system question with connected particles. Parts (a)-(c) involve routine application of Newton's laws and friction (F=μR), with the acceleration calculation being straightforward simultaneous equations. Part (d) requires basic conceptual understanding of what happens when the string breaks, but this is a common exam scenario requiring only simple reasoning about forces. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Diagram with forces \(R\), \(P\), \(T\), \(F\), \(W\) correctly labelled | B1 | Accept \(mg\), \(0.4g\) or \(3.92\) for weight; arrows and labels needed |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(F = 0.5 \times (0.4 \times 9.8)\) | M1 | Need to see \(0.4 \times 9.8\) or \(3.92\) used |
| \(F = 1.96\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(T - 1.96 = 0.4a\) | M1A1 | Consistent reversal of signs in both equations 4 marks; reversal of signs in one equation M1 A1 M1 A0 |
| \(0.3g - T = 0.3a\) | M1A1 | Sign change needs justification (whole string equation: \(0.3g - 1.96 = 0.7a\), M1A1, \(a = 1.4\) A1) max 3/5 |
| \(a = 1.4 \text{ ms}^{-2}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(v = 1.4 \times 3\) | M1 | Full method |
| \(v = 4.2 \text{ ms}^{-2}\) | A1 | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(P\): Friction will cause speed to decrease | M1, A1 | Accept decelerate or comes to rest |
| \(Q\): Gravity will cause speed to increase | M1, A1 | Accept accelerate |
## Question 5:
### Part (a)(i)
| Working | Marks | Guidance |
|---------|-------|----------|
| Diagram with forces $R$, $P$, $T$, $F$, $W$ correctly labelled | B1 | Accept $mg$, $0.4g$ or $3.92$ for weight; arrows and labels needed | **Total: 1** |
### Part (a)(ii)
| Working | Marks | Guidance |
|---------|-------|----------|
| $F = 0.5 \times (0.4 \times 9.8)$ | M1 | Need to see $0.4 \times 9.8$ or $3.92$ used |
| $F = 1.96$ N | A1 | | **Total: 2** |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $T - 1.96 = 0.4a$ | M1A1 | Consistent reversal of signs in both equations 4 marks; reversal of signs in one equation M1 A1 M1 A0 |
| $0.3g - T = 0.3a$ | M1A1 | Sign change needs justification (whole string equation: $0.3g - 1.96 = 0.7a$, M1A1, $a = 1.4$ A1) max 3/5 |
| $a = 1.4 \text{ ms}^{-2}$ | A1 | | **Total: 5** |
### Part (c)
| Working | Marks | Guidance |
|---------|-------|----------|
| $v = 1.4 \times 3$ | M1 | Full method |
| $v = 4.2 \text{ ms}^{-2}$ | A1 | CAO | **Total: 2** |
### Part (d)
| Working | Marks | Guidance |
|---------|-------|----------|
| $P$: Friction will cause speed to decrease | M1, A1 | Accept decelerate or comes to rest |
| $Q$: Gravity will cause speed to increase | M1, A1 | Accept accelerate | **Total: 4** |
---5 A small block $P$ is attached to another small block $Q$ by a light inextensible string. The block $P$ rests on a rough horizontal surface and the string hangs over a smooth peg so that $Q$ hangs freely, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{cfe0bdbc-35e3-485f-a922-b652a72f4c95-4_222_426_507_810}
The block $P$ has mass 0.4 kg and the coefficient of friction between $P$ and the surface is 0.5 .
The block $Q$ has mass 0.3 kg .
The system is released from rest and $Q$ moves vertically downwards.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Draw a diagram to show the forces acting on $P$.
\item Show that the frictional force between $P$ and the surface has magnitude 1.96 newtons.
\end{enumerate}\item By forming an equation of motion for each block, show that the magnitude of the acceleration of each block is $1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\item Find the speed of the blocks after 3 seconds of motion.
\item After 3 seconds of motion, the string breaks. The blocks continue to move. Comment on how the speed of each block will change in the subsequent motion. For each block, give a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2006 Q5 [14]}}