| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Maximum/minimum tension or reaction |
| Difficulty | Standard +0.3 This is a standard circular motion problem requiring conversion of angular speed to rad/s, application of F=mrω² at top and bottom positions, and consideration of weight. The setup is straightforward with clear maximum/minimum positions, making it slightly easier than average despite being a 6-mark question. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05f Vertical circle: motion including free fall |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\omega = 900 \times \frac{2\pi}{60} = 30\pi\) rad s\(^{-1}\) | B1 | Correct angular speed |
| At top: \(mg + N_{min} = m\omega^2 r\), so \(N_{min} = m\omega^2 r - mg\) | M1 | Equation of motion at top |
| \(N_{min} = 0.8(30\pi)^2(0.3) - 0.8(9.8)\) | A1 | Correct substitution |
| \(N_{min} = 2130\) N (3 s.f.) | A1 | cao |
| At bottom: \(N_{max} - mg = m\omega^2 r\), so \(N_{max} = m\omega^2 r + mg\) | M1 | Equation of motion at bottom |
| \(N_{max} = 0.8(30\pi)^2(0.3) + 0.8(9.8) = 2150\) N (3 s.f.) | A1 | cao |
# Question 5:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\omega = 900 \times \frac{2\pi}{60} = 30\pi$ rad s$^{-1}$ | B1 | Correct angular speed |
| At top: $mg + N_{min} = m\omega^2 r$, so $N_{min} = m\omega^2 r - mg$ | M1 | Equation of motion at top |
| $N_{min} = 0.8(30\pi)^2(0.3) - 0.8(9.8)$ | A1 | Correct substitution |
| $N_{min} = 2130$ N (3 s.f.) | A1 | cao |
| At bottom: $N_{max} - mg = m\omega^2 r$, so $N_{max} = m\omega^2 r + mg$ | M1 | Equation of motion at bottom |
| $N_{max} = 0.8(30\pi)^2(0.3) + 0.8(9.8) = 2150$ N (3 s.f.) | A1 | cao |5 An item of clothing is placed inside a washing machine. The drum of the washing machine has radius 30 cm and rotates, about a fixed horizontal axis, at a constant angular speed of 900 revolutions per minute.
Model the item of clothing as a particle of mass 0.8 kg and assume that the clothing travels in a vertical circle with constant angular speed.
Find the minimum magnitude of the normal reaction force exerted by the drum on the clothing and find the maximum magnitude of the normal reaction force exerted by the drum on the clothing.\\[0pt]
[6 marks]
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\hfill \mbox{\textit{AQA M2 2015 Q5 [6]}}