Dr. Hamel develops a flywheel operated automobile. The car uses a uniform cylind

Question

Dr. Hamel develops a flywheel operated automobile. The car uses a uniform cylindrical flywheel of diameter 1.2 m and a mass of 239 kg. Dr. Hamel wants the car to travel 340 km without needing a flywheel spinup. Assume an average retarding force of 450 N and that the flywheel is 73% efficient.

Determine the angular frequency of the flywheel when it has a full energy charge.
(include units with answer)

Hint #1: Angular frequency has units of rpm or Hz Dr. Hamel develops a flywheel operated automobile. The car uses a uniform cylindrical flywheel of diameter 1.2 m and a mass of 239 kg. Dr. Hamel wants the car to travel 340 km without needing a flywheel spinup. Assume an average retarding force of 450 N and that the flywheel is 73% efficient. Determine the angular frequency of the flywheel when it has a full energy charge. (include units with answer) Hint #1: Angular frequency has units of rpm or Hz

Explanation / Answer

d = 1.2 m

So, r = d/2 = 0.6 m

m = 239 kg

So, moment of inertia of flywheel, I = 0.5*mr^2

Let the startup angular frequency be W

So, energy of the flywheel, U = 0.5*I*W^2 = 0.5*(0.5*mr^2)*W^2

So, U = 0.25*mr^2*W^2

So, the energy converted to be used by the automobile,E = 73 percent of U

So, E = 0.73*(0.25*mr^2*W^2) = 0.183*mr^2W^2

average retarding force, Fr = 450 N

So, energy lost after travelling 340 km(or 340000 m) E,lost= 450*340000 = 1.53*10^8 J

So, By work energy principle,

E = E,lost

So,  0.183*mr^2W^2 = 1.53*10^8

So, W = sqrt(1.53*10^8/(0.183*239*0.6^2))

= 3117 rad/s <------answer

= 2.98*10^4 rpm <--------answer

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