5 The engine of a car of mass 1200 kg produces a maximum power of 40 kW .
In an initial model of the motion of the car the total resistance to motion is assumed to be constant.
- Given that the greatest steady speed of the car on a straight horizontal road is \(42 \mathrm {~ms} ^ { - 1 }\), find the magnitude of the resistance force.
The car is attached to a trailer of mass 200 kg by a light rigid horizontal tow bar. The greatest steady speed of the car and trailer on the road is now \(30 \mathrm {~ms} ^ { - 1 }\). The resistance to motion of the trailer may also be assumed constant.
- Find the magnitude of the resistance force on the trailer.
The car and trailer again travel along the road. At one instant their speed is \(15 \mathrm {~ms} ^ { - 1 }\) and their acceleration is \(0.57 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- (a) Find the power of the engine of the car at this instant.
(b) Find the magnitude of the tension in the tow bar at this instant.
In a refined model of the motion of the car and trailer the resistance to the motion of each is assumed to be zero until they reach a speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the speed is \(10 \mathrm {~ms} ^ { - 1 }\) or above the same constant resistance forces as in the first model are assumed to apply to each.
The car and trailer start at rest on the road and accelerate, using maximum power. - Without carrying out any further calculations,
(a) explain whether the time taken to attain a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) would be predicted to be lower, the same or higher using the refined model compared with the original model,
(b) explain whether the greatest steady speed of the system would be predicted to be lower, the same or higher using the refined model compared with the original model.