| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Two particles over pulley, vertical strings |
| Difficulty | Moderate -0.8 This is a standard M1 pulley problem requiring routine application of Newton's second law to two connected particles. The question guides students through each step (modelling assumption, forming equations, finding tension), making it more straightforward than average. The arithmetic is simple (masses 2kg and 5kg give clean acceleration 4.2 m/s²), and the method is a textbook exercise that all M1 students practice extensively. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution |
| Answer | Marks | Guidance |
|---|---|---|
| Light or smooth | B1 (1) | Acceptable assumption |
| Answer | Marks | Guidance |
|---|---|---|
| \(5g - T = 5a\) | M1, A1 | Three term equation of motion for one particle; Correct equation |
| \(T - 2g = 2a\) | M1, A1 | Three term equation of motion for other particle; Correct equation |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = \frac{3g}{7} = 4.2 \text{ ms}^{-2}\) | A1 (5) | AG; correct acceleration from correct working |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 2\times4.2 + 2\times9.8 = 28 \text{ N}\) | M1, A1 (2) | Substitute \(a=4.2\) into one equation of motion; Correct tension |
## Question 4:
### Part (a)
Light or smooth | B1 (1) | Acceptable assumption
### Part (b)
$5g - T = 5a$ | M1, A1 | Three term equation of motion for one particle; Correct equation
$T - 2g = 2a$ | M1, A1 | Three term equation of motion for other particle; Correct equation
$3g = 7a$
$a = \frac{3g}{7} = 4.2 \text{ ms}^{-2}$ | A1 (5) | AG; correct acceleration from correct working
### Part (c)
$T = 2\times4.2 + 2\times9.8 = 28 \text{ N}$ | M1, A1 (2) | Substitute $a=4.2$ into one equation of motion; Correct tension
---4 Two particles are connected by a string, which passes over a pulley. Model the string as light and inextensible. The particles have masses of 2 kg and 5 kg . The particles are released from rest.\\
\includegraphics[max width=\textwidth, alt={}, center]{eb1f2470-aeeb-4b1d-a6c0-bdeb7048edd5-3_392_209_1685_909}
\begin{enumerate}[label=(\alph*)]
\item State one modelling assumption that you should make about the pulley in order to determine the acceleration of the particles.
\item By forming an equation of motion for each particle, show that the magnitude of the acceleration of each particle is $4.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\item Find the tension in the string.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q4 [8]}}