| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.3 This is a standard M2 circular motion problem with two strings. Part (a) is direct application of a=v²/r, part (b) requires resolving forces vertically and horizontally with given answer to verify, and part (c) follows immediately. The geometry is straightforward (right-angled triangle), and all steps are routine applications of Newton's second law in circular motion. Slightly easier than average due to the 'show that' scaffold in part (b). |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(= \frac{2^2}{0.2} = 20\) m s\(^{-2}\) | M1 A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(T_1 = 45.3\) N | B1 M1 A1 A1 | 4 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(T_2 = 57.4\) N | M1A1 A1 | 3 marks |
**(a)** Acceleration is $\frac{v^2}{r}$
$= \frac{2^2}{0.2} = 20$ m s$^{-2}$ | M1 A1 | 2 marks
**(b)** $\theta = 30°$
Resolve vertically:
$T_1 \cos \theta = mg$
$T_1 \cos \theta = 4g$
$T_1 = 45.3$ N | B1 M1 A1 A1 | 4 marks | AG
**(c)** Resolve horizontally:
$T_1 \sin \theta + T_2 = \frac{mv^2}{r}$
$45.3\sin \theta + T_2 = 4 \times 20$
$T_2 = 57.4$ N | M1A1 A1 | 3 marks | M1 for 3 terms, 2 correct; Condone 57.3 N
**Total: 9 marks**
---5 Two light inextensible strings, of lengths 0.4 m and 0.2 m , each have one end attached to a particle, $P$, of mass 4 kg . The other ends of the strings are attached to the points $A$ and $B$ respectively. The point $A$ is vertically above the point $B$. The particle moves in a horizontal circle, centre $B$ and radius 0.2 m , at a speed of $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The particle and strings are shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{1bc18163-b20e-4dc6-bd35-496efec8dc73-4_396_558_587_735}
$$\text { ← } 0.2 \mathrm {~m} \longrightarrow$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the magnitude of the acceleration of the particle.
\item Show that the tension in string $P A$ is 45.3 N , correct to three significant figures.
\item Find the tension in string $P B$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2008 Q5 [9]}}