It has been argued that power plants should make use of off-peak hours (such as
ID: 2206691 • Letter: I
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 it until it is needed during peak load times, such as the middle of 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 7800kg/m^3, in the shape of a uniform disk with a thickness of 12.4cm.
a) What would the diameter of such a disk need to be if it is to store an amount of kinetic energy of 12.4MJ when spinning at an angular velocity of 92.0rpm about an axis perpendicular to the disk at its center?
b) What would the centripetal acceleration of a point on its rim when spinning at this rate?
Explanation / Answer
for the flywheel I=m*r^2/2 90 rpm is ?=90*2*p/60 rad/sec or 3*p rad/sec KE of the flywheel is .5*I*?^2 12.4^7 J=.5m*r^2*9*p^2/2 since the flywheel is 12.4 cm thick, the volume of the flywheel is p*r^2*0.10 m^3 knowing the density m=7800*p*r^2*0.124 kg 12.4^7=7800*p*r^2*0.10*r^2*9*p^2/4 solve for r r=3.68 m diameter = r*2=7.36 m check mass is 7800*3.14*3.68^2*0.10 33227 kg I=33227*2.6^2/2 I=225387 KE=.5*225387*9*3.14^2 b) centripetal acceleration is -?^2*r =-9*3.14^2*3.68 -326.6 m/s^2
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