M2 June 2009 Q3
3. A truck of mass of 300 kg moves along a straight horizontal road with a constant speed of 10 m s\(^{-1}\). The resistance to motion of the truck has magnitude 120 N.
(a) Find the rate at which the engine of the truck is working. (2)
On another occasion the truck moves at a constant speed up a hill inclined at \(\theta\) to the horizontal, where \(\sin\theta = \dfrac{1}{14}\). The resistance to motion of the truck from non-gravitational forces remains of magnitude 120 N. The rate at which the engine works is the same as in part (a).
(b) Find the speed of the truck. (4)
| Scheme | Marks |
|---|---|
| Constant v \(\Rightarrow\) driving force = resistance \(\Rightarrow F = 120\) (N) | M1 |
| \(\Rightarrow P = 120 \times 10 = 1200\) W | M1 |
| (2) |
| Scheme | Marks |
|---|---|
| Resolving parallel to the slope, zero acceleration: | |
| \(\dfrac{P}{v} = 120 + 300g\sin\theta\ (= 330)\) | M1A1A1 |
| \(\Rightarrow v = \dfrac{1200}{330} = 3.6\) (m s\(^{-1}\)) | A1 |
| (4) | |
| (6 marks) |