Abus contains a 1500 kg, 0.600 m radius flywheel (a disk) and has a total mass of 10,000 kg.
(a) calculate the angular velocity the flywheel must have, in rad/s, to contain enough energy to take the bus from rest to a speed of 24.5 m/s, assuming 85.0% of the rotational kinetic energy can be transformed into translational energy
(b) how high a hill, in meters, can the bus climb with this stored energy and still have a speed of 5.00 m/s at the top of the hill?

Explanation:

Given that,

Mass of the bus, m = 1500 kg

Mass of the flywheel, M = 10,000 kg

Radius of flywheel, r = 0.6 m

Speed of the bus, v = 24.5 m/s

(a) Let is the angular velocity of the flywheel. It is assumed that 85.0% of the rotational kinetic energy can be transformed into translational energy. Using the conservation of energy as :

(b) Let h is the height climb with this stored energy. Again using the conservation of energy as :

h = 15.31 meters

Hence, this is the required solution.

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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