In a city with an air-pollution problem, a bus has no combustion engine. It runs
ID: 1607318 • Letter: I
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 5600 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 0.700 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
here,
mass of flywheel, m = 1600 kg
radius of flywheel, r = 0.7 m
average power, p = 18 hp = 18*745.7 = 13422.6 watts
angular angular speed, w = 5600 rev/min = 586.431 rad/s
average speed, v = 40 km/hr = 40*1000/3600 = 11.11 m/s
Total kinetic energy of system:Ket
Ket = 0.5 * I * w^2
Ket = 0.5 * 0.5 * m * r^2 * w^2
Ket = 0.5 * 0.5 * 1600 * 0.7^2 * 586.431^2
Ket = 6.740 * 10^7 J
Time for operation of wheel, t = Ket/Power
Time for operation of wheel, t = 6.740 * 10^7/13422.6
Time for operation of wheel, t = 5021.382 s
Distance, d = speed * time
Distance, d = 11.11 * 5021.382
Distance, d = 55.787 km