It has been argued that power plants should make use of off-peak hours (such as

Question

It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store H until it is needed during peak load times, such as the middle 6f the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball-bearings. Consider a flywheel made of iron, with a density of 7800 kg, mn in the shape of a uniform d.sk with a thickness of 10.2 What would the diameter of such o risk need to be if it is to store an amount of kinetic energy of 10.0 MJ when sprang at an angular velocity of 93.0 rpm about an axis perpendicular to tot dirt at its center What would be the centripetal acceleration of a point on its rim when at this rate?

Explanation / Answer

density = d = 7800 kg /m^3

angular speed = w = 93 rpm = 93*(2*pi/60 = 9.74 rad/s

kinetic energy = 10*10^6 J

thickness = t = 10.2 cm = 0.102 m

area = A = pi*r^2

volume = A*t = pi*r^2*t

mass of the fly wheel = m = d*V = d*pi*r^2*t

moment of inertia of fly wheel = I + 0.5*m*r^2

kinetic energy = 0.5*I*w^2

K = 0.5*0.5*d*pi*r^2*w^2

10*10^6 = 0.5*0.5*7800*pi*r^2*9.73^2

radius = r = 4.15 m

diameter = D = 2r = 8.3 m <<------------------answer

part(B)

centripetal acceleration = a = r*w^2

a = 4.15*9.73^2 = 392.8 m/s^2 <<--------answer

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