A flywheel consists of a uniform steel disk of diameter 0.3 m and thickness of 0.1 m . This flywheel is used in a car as a means of energy storage and propulsion and is connected to the drivetrain which has an efficiency of 0.92 .
a) If the car requires 8 kW of power to cruise at 70 mph on a highway with no slope, find the range of the car if powered only by the flywheel which is initially rotating at 30,000rpm, with minimum allowable flywheel speed of 1,000rpm.
b) The flywheel is initially at 24,000rpm and the minimum allowable flywheel speed is 1,000rpm. If the flywheel is used to drive the car uphill on a road with a slope of 4\deg , what is the maximum distance the car can drive uphill if air and rolling frictions are negligible? Consider the total weight of the car to be 1,800kg.