Problem: Flywheels are large, massive wheels used to store energy. They can be s

Question

Problem:

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 2.0 mdiameter and a mass of 220 kg . Its maximum angular velocity is 1400 rpm .

Part C

The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.5 s . What is the average power delivered to the machine?

Express your answer to two significant figures and include the appropriate units.

Part D

How much torque does the flywheel exert on the machine?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The maximum angular velocity is ( 1400*2* / 60 ) = 146.61 rad/s

The moment of inertia comes into play here, and the torque is:

= I*

For a solid cylinder, the moment of inertia is:

I = (1/2)*m*r^2 = (1/2)*220*(2/2)^2 = 110 kg*m^2

The energy stored is:

E = (1/2)*I*^2 = (1/2)*110*( 146.61 )^2 = 1.182 x 10^6 J

The power is dW/dt or W/t

P = ( 1.182 x 10^6 / 2 ) / 2.5 = 2.4 x 10^5 W

Half of the energy is lost, so we can calculate the angular velocity after power delivery:

E2 = ( 1.182 x 10^6 / 2 ) = (1/2)*I*(2)^2

2 = sqrt[ ( 1.182 x 10^6 ) / 110 ] = 103.66 rad/s

The angular acceleration during power delivery is:

= /t = (146.61 - 103.66) / 2.5 = 17.18 rad/s^2

The torque is:

= I* = 110 * 17.18 = 1889.8 Nm = 1900 Nm (approx)

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