| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Horizontal circular track – friction only (no banking) |
| Difficulty | Moderate -0.8 This is a straightforward application of circular motion formulas (F = mv²/r) and friction (F ≤ μR). Both parts are 'show that' questions with given answers, requiring only direct substitution of values and simple algebraic manipulation. No problem-solving insight or novel approach needed—purely routine mechanics calculation below typical A-level standard. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(a = \frac{14^2}{50} = 3.92\) and \(F = 1200 \times 3.92 = 4704 \text{ N}\) | M1, A1, dM1, A1 | 4 marks |
| (b) \(R = 1200 \times 9.8 = 11760\) | B1 | — |
| \(4704 \leq \mu \times 11760\) and \(\mu \geq \frac{4704}{11760}\), so \(\mu \geq 0.4\) | M1, A1 | 3 marks |
**(a)** $a = \frac{14^2}{50} = 3.92$ and $F = 1200 \times 3.92 = 4704 \text{ N}$ | M1, A1, dM1, A1 | 4 marks | Finding acceleration; correct acceleration; use of $F = ma$; correct force from correct working
**(b)** $R = 1200 \times 9.8 = 11760$ | B1 | — | Normal reaction
$4704 \leq \mu \times 11760$ and $\mu \geq \frac{4704}{11760}$, so $\mu \geq 0.4$ | M1, A1 | 3 marks | Applying $F \leq \mu R$ or $F = \mu R$; correct result from correct working
**Total for Question 6: 7 marks**
---6 A car of mass 1200 kg travels round a roundabout on a horizontal, circular path at a constant speed of $14 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The radius of the circle is 50 metres. Assume that there is no resistance to the motion of the car and that the car can be modelled as a particle.
\begin{enumerate}[label=(\alph*)]
\item A friction force, directed towards the centre of the roundabout, acts on the car as it moves. Show that the magnitude of this friction force is 4704 N .
\item The coefficient of friction between the car and the road is $\mu$. Show that $\mu \geqslant 0.4$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2006 Q6 [7]}}