| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Three or more connected particles |
| Difficulty | Moderate -0.3 This is a straightforward two-part pulley problem requiring basic equilibrium analysis and then Newton's second law. Part (a) involves simple force balance (tension equals weight of heavier particle, then resolve forces on A), while part (b) is a standard connected particles calculation using F=ma. The setup is clearly defined with no geometric complications, making it slightly easier than average but still requiring proper method. |
| Spec | 3.03b Newton's first law: equilibrium3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 6 \times 9.8 = 58.8\) N | B1 | Use of tension being equal to the weight. Accept 6g |
| Answer | Marks | Guidance |
|---|---|---|
| \(58.8 = T + 4 \times 9.8\) | M1, A1 | Three term equation for equilibrium containing 58.8, \(T\) and 4×9.8 or equivalent terms. For M1, 58.8 can be replaced by candidates answer to part (a)(i) provided it is not zero. Correct equation. |
| \(T = 58.8 - 39.2 = 19.6\) N | A1 | Correct tension. Accept 2g |
| Answer | Marks | Guidance |
|---|---|---|
| \(6g - T = 6a\) | M1, A1 | Three term equation of motion for 6 kg particle containing 58.8 or 6g, \(T\) and 6a. Correct equation. |
| \(T - 4g = 4a\) | M1, A1 | Three term equation of motion for 4 kg particle containing 39.2 or 4g, \(T\) and 4a. Correct equation. |
| \(2g = 10a\) | ||
| \(a = 1.96\) ms\(^{-2}\) | A1 | Correct acceleration. Candidates who work consistently to obtain \(a = -1.96\) gain full marks. |
**3(a)(i)**
| $T = 6 \times 9.8 = 58.8$ N | B1 | Use of tension being equal to the weight. Accept 6g |
**3(a)(ii)**
| $58.8 = T + 4 \times 9.8$ | M1, A1 | Three term equation for equilibrium containing 58.8, $T$ and 4×9.8 or equivalent terms. For M1, 58.8 can be replaced by candidates answer to part (a)(i) provided it is not zero. Correct equation. |
| $T = 58.8 - 39.2 = 19.6$ N | A1 | Correct tension. Accept 2g |
**3(b)**
| $6g - T = 6a$ | M1, A1 | Three term equation of motion for 6 kg particle containing 58.8 or 6g, $T$ and 6a. Correct equation. |
| $T - 4g = 4a$ | M1, A1 | Three term equation of motion for 4 kg particle containing 39.2 or 4g, $T$ and 4a. Correct equation. |
| $2g = 10a$ | | |
| $a = 1.96$ ms$^{-2}$ | A1 | Correct acceleration. Candidates who work consistently to obtain $a = -1.96$ gain full marks. |3 Two particles, $A$ and $B$, have masses 4 kg and 6 kg respectively. They are connected by a light inextensible string that passes over a smooth fixed peg. A second light inextensible string is attached to $A$. The other end of this string is attached to the ground directly below $A$. The system remains at rest, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{a381686b-0b1e-41ba-b88f-be1601e42098-3_457_711_523_845}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Write down the tension in the string connecting $A$ and $B$.
\item Find the tension in the string connecting $A$ to the ground.
\end{enumerate}\item The string connecting particle $A$ to the ground is cut. Find the acceleration of $A$ after the string has been cut.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2008 Q3 [9]}}