| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Vertical circle: speed at specific point |
| Difficulty | Standard +0.3 This is a standard vertical circle problem requiring conservation of energy between two points and Newton's second law for circular motion. The steps are routine: apply energy conservation from B to A, then use T - mg = mv²/r at the lowest point. While it involves two parts and careful algebra, it follows a well-practiced template with no novel insight required, making it slightly easier than average. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05e Radial/tangential acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = \sqrt{13ag}\) | M1A1 A1 A1 | 4 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 14mg\) | M1A1 m1 A1ft | 4 marks |
**(a)** Conservation of energy:
$\frac{1}{2}m(3\sqrt{ag})^2 + mg \cdot 2a = \frac{1}{2}mv^2$
$\frac{9}{2}mga + 2mga = \frac{1}{2}mv^2$
$v = \sqrt{13ag}$ | M1A1 A1 A1 | 4 marks | M1 for 3 terms: 2 KE and PE
**(b)** At A, consider vertical forces:
$T - mg = \frac{mv^2}{a}$
$T = mg + 13mg$
$T = 14mg$ | M1A1 m1 A1ft | 4 marks | M1 for 3 terms, 2 correct; ft from (a)
**Total: 8 marks**
---7 A light inextensible string, of length $a$, has one end attached to a fixed point $O$. A particle, of mass $m$, is attached to the other end. The particle is moving in a vertical circle, centre $O$. When the particle is at $B$, vertically above $O$, the string is taut and the particle is moving with speed $3 \sqrt { a g }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{1bc18163-b20e-4dc6-bd35-496efec8dc73-5_422_399_497_778}
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $g$ and $a$, the speed of the particle at the lowest point, $A$, of its path.
\item Find, in terms of $g$ and $m$, the tension in the string when the particle is at $A$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2008 Q7 [8]}}