A passenger bus in Zurich. Switzerland derived its motive power from the energy

Question

A passenger bus in Zurich. Switzerland derived its motive power from the energy stored in a large flywheel. The wheel was brought up to speed periodically, when the bus stopped at a station, by an electric motor, which could then be attached to the electric power lines. The flywheel was a solid cylinder with a mass of 1100 kg and a diameter of 1.78 m: its top angular speed was 3100 rev/min. At this angular speed, what is the kinetic energy of the flywheel? Part B If the average power required to operate the bus is 1.9 times 10^4 W. how long could it operate between stops?

Explanation / Answer

given data

m=1100kg

diameter=1.78 m

radius =0.89m

angular speed =3100rev/min

avg power = 1.90*10^4 W

  part A ) from rotational dynamics
moment of inertia is
I=1/2mR^2
angular velocity
w=3100(2*pi/60)

K=1/2*I*w^2 =1/2*1/2mR^2 *w^2

K=0.5*0.5*1100*1.78*1.78*3100*3100*4*3.14*3.14/3600 = 9.2*10^7 J

Part B )

= KE/power = 9.2*10^7 /1.9*10^4 = 4842 J/W

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