7. A car of mass 1250 kg tows a caravan of mass 850 kg up a hill inclined at an angle \(\alpha\) to the horizontal where \(\sin \alpha = \frac { 1 } { 14 }\). The total resistance to motion experienced by the car is 400 N , and by the caravan is 500 N .
Given that the driving force of the engine is 3 kN ,
- show that the acceleration of the system is \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
- find the tension in the towbar linking the car and the caravan.
Starting from rest, the car accelerates uniformly for 540 m until it reaches a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the top of the hill.
- Find v.
At the top of the hill the road becomes level and the driver maintains the speed at which the car and caravan reached the top of the hill.
- Assuming that the resistance to motion on each part of the system is unchanged, find the percentage reduction in the driving force of the engine required to achieve this.