M1 June 2009 Q4
4. A small brick of mass 0.5 kg is placed on a rough plane which is inclined to the horizontal at an angle \(\theta\), where \(\tan\theta = \tfrac{4}{3}\), and released from rest. The coefficient of friction between the brick and the plane is \(\tfrac{1}{3}\).
Find the acceleration of the brick. (9)
| Scheme | Marks |
|---|---|
| \(0.5g\sin\theta - F = 0.5a\) | M1 A1 A1 |
| \(F = \tfrac{1}{3}R\) seen | B1 |
| \(R = 0.5g\cos\theta\) | M1 A1 |
| Use of \(\sin\theta = \tfrac{4}{5}\) or \(\cos\theta = \tfrac{3}{5}\) or decimal equiv or decimal angle e.g. \(53.1^\circ\) or \(53^\circ\) | B1 |
| \(a = \dfrac{3g}{5}\) or 5.88 m s\(^{-2}\) or 5.9 m s\(^{-2}\) | DM1 A1 |
| (9 marks) |