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ziro4ka
2 months ago
6

A bus is designed to draw its power from a rotating flywheel that is brought up to 3000 rpm by an electric motor. The flywheel i

s a solid cylinder of mass 2000 kg and diameter 1 m. If the bus requires an average power of 20 kilowatts, how long will the flywheel rotate?
620 s

830 s

980 s

1,200 s

2,500 s
Physics
1 answer:
Yuliya22 [3.3K]2 months ago
3 0

To tackle this problem, we will use the concept of rotational kinetic energy. After determining this energy, we will find the time based on the power definition, which indicates how energy changes over time. Let's begin with the formula for the kinetic energy of a rotating flywheel:

E_r = \frac{1}{2} I\omega^2

Where

I = moment of inertia

\omega = Angular velocity

In this scenario, we have:

\omega = 3000\frac{rev}{min}(\frac{2\pi rad}{1rev})(\frac{1min}{60s})

\omega = 314.159rad/s

Substituting the moment of inertia values for this object yields:

E_r = \frac{1}{2} (\frac{MR^2}{2})\omega^2

E_r = \frac{1}{2} (\frac{2000(0.5)^2}{2})(314.159)^2

E_r = 1.233698*10^7J

The average power expression is given by:

P = \frac{E_r}{\Delta t}

\Delta t = \frac{E_r}{P}

\Delta t = \frac{1.233698*10^7}{20*10^3}

\Delta t = 616.8s \approx 620s

Hence, the correct conclusion is 620 seconds.

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Explanation:

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