| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 13 |
| 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 M1 pulley system question requiring routine application of Newton's second law and friction concepts. While it involves multiple parts and connected particles, the steps are straightforward: calculate acceleration from kinematics (given), apply F=ma to each mass separately, and solve for tension and friction coefficient. No novel insight or complex problem-solving required—typical textbook exercise slightly easier than average A-level due to being given the final speed explicitly. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| The string is light and inextensible or inelastic or taut | B1 | First assumption |
| B1 | Total: 2 — Second assumption |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(6 = 0 + 4a\) | M1 | Finding \(a\) using a constant acceleration equation |
| \(a = \frac{6}{4} = 1.5\) | A1 | Total: 2 — Correct \(a\) from correct working |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(7 \times 9.8 - T = 7 \times 1.5\) | M1 A1 | Three term equation of motion with \(F\) for the 7 kg particle. Correct equation |
| \(T = 68.6 - 10.5 = 58.1\) | A1 | Total: 3 — Correct tension |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(58.1 - F = 13 \times 1.5\) | M1 A1 | Three term equation of motion with \(F\) for the 13 kg particle. Correct equation |
| \(F = 58.1 - 19.5 = 38.6\) | A1 | Correct \(F\) |
| \(R = 13.98 \approx 127.4\) | B1 | Correct \(R\) |
| \(38.6 = \mu \times 127.4\) | dM1 | Use of \(F = \mu R\) |
| \(\mu = \frac{38.6}{127.4} = 0.303\) | A1 | Total: 6 — Correct coefficient of friction |
## Question 4:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| The string is light and inextensible or inelastic or taut | B1 | First assumption |
| | B1 | **Total: 2** — Second assumption |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $6 = 0 + 4a$ | M1 | Finding $a$ using a constant acceleration equation |
| $a = \frac{6}{4} = 1.5$ | A1 | **Total: 2** — Correct $a$ from correct working |
### Part (c)
| Working | Marks | Guidance |
|---------|-------|----------|
| $7 \times 9.8 - T = 7 \times 1.5$ | M1 A1 | Three term equation of motion with $F$ for the 7 kg particle. Correct equation |
| $T = 68.6 - 10.5 = 58.1$ | A1 | **Total: 3** — Correct tension |
### Part (d)
| Working | Marks | Guidance |
|---------|-------|----------|
| $58.1 - F = 13 \times 1.5$ | M1 A1 | Three term equation of motion with $F$ for the 13 kg particle. Correct equation |
| $F = 58.1 - 19.5 = 38.6$ | A1 | Correct $F$ |
| $R = 13.98 \approx 127.4$ | B1 | Correct $R$ |
| $38.6 = \mu \times 127.4$ | dM1 | Use of $F = \mu R$ |
| $\mu = \frac{38.6}{127.4} = 0.303$ | A1 | **Total: 6** — Correct coefficient of friction |
---4 The diagram shows a block, of mass 13 kg , on a rough horizontal surface. It is attached by a string that passes over a smooth peg to a sphere of mass 7 kg , as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{965a176a-848c-478d-a748-80fc9dfe4399-3_323_974_1256_575}
The system is released from rest, and after 4 seconds the block and the sphere both have speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and the block has not reached the peg.
\begin{enumerate}[label=(\alph*)]
\item State two assumptions that you should make about the string in order to model the motion of the sphere and the block.
\item Show that the acceleration of the sphere is $1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\item Find the tension in the string.
\item Find the coefficient of friction between the block and the surface.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2007 Q4 [13]}}