6. A car of mass 1200 kg pulls a trailer of mass 400 kg up a straight road which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 1 } { 14 }\). The trailer is attached to the car by a light inextensible towbar which is parallel to the road. The car's engine works at a constant rate of 60 kW . The non-gravitational resistances to motion are constant and of magnitude 1000 N on the car and 200 N on the trailer.
At a given instant, the car is moving at \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
- the acceleration of the car at this instant,
- the tension in the towbar at this instant.
The towbar breaks when the car is moving at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find, using the work-energy principle, the further distance that the trailer travels before coming instantaneously to rest.