M3 January 2009 Q3
3. A rough disc rotates about its centre in a horizontal plane with constant angular speed 80 revolutions per minute. A particle \(P\) lies on the disc at a distance 8 cm from the centre of the disc. The coefficient of friction between \(P\) and the disc is \(\mu\). Given that \(P\) remains at rest relative to the disc, find the least possible value of \(\mu\). (7)
| Scheme | Marks |
|---|---|
| \(\omega = \dfrac{80 \times 2\pi}{60}\) rad s\(^{-1}\) \(\left(= \dfrac{8\pi}{3} \approx 8.377\ldots\right)\) Accept \(v = \dfrac{16\pi}{75} \approx 0.67\) ms\(^{-1}\) as equivalent | B1 |
| \((\uparrow)\) \(R = mg\) | B1 |
| For least value of \(\mu\) \((\leftarrow)\) \(\mu mg = mr\omega^2\) | M1 A1=A1 |
| \(\mu = \dfrac{0.08}{9.8} \times \left(\dfrac{8\pi}{3}\right)^2 \approx 0.57\) accept 0.573 | M1 A1 |
| (7) | |
| (7 marks) |