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 1070 kg and a diameter of 1.70 m ; its top angular speed was 2970 rev/min . 1. At this angular speed, what is the kinetic energy of the flywheel? 2. If the average power required to operate the bus is 1.89

Answer 1

Answer:

18695271.3209 J

989.167794757 s

Explanation:

r = Radius = $\dfrac{1.7}{2}=0.85\ m$

N = 2970 rpm

m = Mass of flywheel = 1070 kg

P = Power = $1.89\times 10^4\ W$

Moment of inertia

$I=\dfrac{1}{2}mr^2\\\Rightarrow I=\dfrac{1}{2}1070\times 0.85^2\\\Rightarrow I=386.5375\ kgm^2$

Angular speed

$\omega=2970\times \dfrac{2\pi}{60}\\\Rightarrow \omega=311.017672705\ rad/s$

Kinetic energy

$K=\dfrac{1}{2}I\omega^2\\\Rightarrow K=\dfrac{1}{2}386.5375\times 311.017672705^2\\\Rightarrow K=18695271.3209\ J$

The kinetic energy is 18695271.3209 J

Time is given by

$t=\dfrac{E}{P}\\\Rightarrow t=\dfrac{18695271.3209}{1.89\times 10^4}\\\Rightarrow t=989.167794757\ s$

The time taken is 989.167794757 s