M1 January 2013 Q4
4. A lifeboat slides down a straight ramp inclined at an angle of 15\(^\circ\) to the horizontal. The lifeboat has mass 800 kg and the length of the ramp is 50 m. The lifeboat is released from rest at the top of the ramp and is moving with a speed of 12.6 m s\(^{-1}\) when it reaches the end of the ramp. By modelling the lifeboat as a particle and the ramp as a rough inclined plane, find the coefficient of friction between the lifeboat and the ramp. (9)
| Scheme | Marks |
|---|---|
| \(12.6^2 = 2a.50\) \((\Rightarrow a = 1.5876)\) | M1 A1 |
| \(800g\sin 15 - F = 800a\) | M1 A1 |
| \(R = 800g\cos 15\) | M1 A1 |
| \(F = \mu R\) | B1 |
| \(800g\sin 15 - \mu 800g\cos 15 = 800 \times 1.5876\) | M1 |
| \(\mu = 0.1,\ 0.10,\ 0.100\) | A1 |
| (9 marks) |