Flywheels are large, massive wheels used to store energy. They can be spun up sl

Question

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 1.5 m diameter and a mass of 240 kg . Its maximum angular velocity is 1600 rpm .

Part A

A motor spins up the flywheel with a constant torque of 60 Nm . How long does it take the flywheel to reach top speed?

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

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Part B

How much energy is stored in the flywheel?

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

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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 2.3 s . What is the average power delivered to the machine?

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

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Part D

How much torque does the flywheel exert on the machine?

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

t = Item 17 Part A 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 1.5 m diameter and a mass of 240 kg. Its maximum angular velocity is 1600 rpm A motor spins up the flywheel with a constant torque of 60 N m. How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units t=1 Value Units Submit My Answers Give Up Incorrect, Iry Again, 25 attempts remaining Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units E= Value Units Submit My Answers Give Up Incorrect, Iry Again, 27 attempts remaining 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 2.3 s . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units P= Value Units

Explanation / Answer

Torque is T = I*alpha

I is the moment of inertia = (1/2)*M*R^2 = 0.5*240*(1.5/2)^2 = 67.5 kg-m^2

alpha is the anguar accelaration = (w/t)

w = 1600 rpm = 1600*(2*3.142/60) = 167.57 rad/s

then

T = I*alpha

60 = 67.5*(167.57/t)

t = 188.5 sec

B) KE = 0.5*I*w^2 = 0.5*67.5*167.57^2 = 9.48*10^5 J

C) P = (0.5*KE)/t = (0.5*9.48*10^5)/2.3 = 2.06*10^5 W

D) P = T*w

P = 0.5*(0.5*I*w^2)/t

2.06*10^5 = (0.5*0.5*67.5*w^2)/2.3

w = 167.56 rad/s

then

P = T*w

2.06*10^5 = T*167.56

T = 1230 N-m

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