Question
In a city with an air-pollution problem, a bus has no combustion engine. It runs on energy drawn from a large, rapidly rotating flywheel under the floor of the bus. The flywheel is spun up to its maximum rotation rate of 5400 rev/min by an electric motor at the bus terminal. Every time the bus speeds up, the flywheel slows down slightly. The bus is equipped with regenerative braking so that the flywheel can speed up when the bus slows down. The flywheel is a uniform solid cylinder with mass 1600 kg and radius 0.800 m. The bus body does work against air resistance and rolling resistance at the average rate of 18.0 hp as it travels with an average speed of 40.0 km/h. How far can the bus travel before the flywheel has to be spun up to speed again?
Explanation / Answer
Given data Angular velocity of the wheel is, = 5200 rev/min = (5200 rev /min) (2 rad /1 rev) (1 min /60 s) = 544.54 rad/s Mass of the solid cylinder is, m = 1600 kg Radius of the solid cylinder is, r = 0.650 m Power, P = 18.0 hp = (18.0 hp) (746 W) = 13428 W Average speed, v = 40 km/h = (40 km/h) (5/18) = 11.1 m/s Moment of inertia of the solid cylinder is, I = 1/2 mr2 Kinetic energy of the wheel is, E = (1/2) I 2 Solution: Power output of the bus is, P = E / t = (1/2) I 2 / (d / v) d = (1/2 )(1/2 ) mr2 2v / P = (1600 kg) (0.650 m)2 (544.54 rad/s)2 (11.1 m/s) / 4 (13428 W ) = 4.14 * 104 m or 41.4 km