| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Mechanics (Further Paper 3 Mechanics) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Moderate -0.5 This is a standard conical pendulum problem requiring resolution of forces and application of circular motion equations. Part (a) is a 'show that' using vertical equilibrium (T cos 30° = mg), part (b) applies horizontal circular motion (T sin 30° = mrω²), and part (c) tests understanding of modelling assumptions. While it's Further Maths content, the problem-solving is routine and methodical with no novel insight required, making it slightly easier than average. |
| Spec | 3.03f Weight: W=mg3.03m Equilibrium: sum of resolved forces = 06.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.4 \times 9.8 = T\cos 30°\) | M1 | Resolves vertically to form equation for tension |
| \(T = 4.5\text{ N}\) | A1 | Correct tension |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = 0.6\sin 30° = 0.3\) | B1 | Finds radius |
| \(T\sin 30° = 0.4 \times r\omega^2\) | M1 | Forms equation using their radius and tension |
| \(\omega = \sqrt{\dfrac{4.5\sin 30°}{0.4 \times 0.3}} = 4.3\text{ rad s}^{-1}\) | A1F | Correct angular speed to 2 sf; FT if both M1 marks awarded |
| Answer | Marks | Guidance |
|---|---|---|
| Light and inextensible | B1 | Two appropriate assumptions stated |
## Question 5:
### Part (a):
| $0.4 \times 9.8 = T\cos 30°$ | M1 | Resolves vertically to form equation for tension |
| $T = 4.5\text{ N}$ | A1 | Correct tension |
### Part (b):
| $r = 0.6\sin 30° = 0.3$ | B1 | Finds radius |
| $T\sin 30° = 0.4 \times r\omega^2$ | M1 | Forms equation using their radius and tension |
| $\omega = \sqrt{\dfrac{4.5\sin 30°}{0.4 \times 0.3}} = 4.3\text{ rad s}^{-1}$ | A1F | Correct angular speed to 2 sf; FT if both M1 marks awarded |
### Part (c):
| Light and inextensible | B1 | Two appropriate assumptions stated |
---5 In this question use $\boldsymbol { g } = 9.8 \mathbf { m ~ s } ^ { \mathbf { - 2 } }$.\\
A conical pendulum consists of a string of length 60 cm and a particle of mass 400 g . The string is at an angle of $30 ^ { \circ }$ to the vertical, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{4fdb2637-6368-422c-99da-85b80efe31c5-08_501_606_644_854}
5
\begin{enumerate}[label=(\alph*)]
\item Show that the tension in the string is 4.5 N .
5
\item Find the angular speed of the particle.\\[0pt]
[3 marks]\\
5
\item State two assumptions that you have made about the string.
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics Q5 [6]}}