Question

Humanity uses energy at the rate of about 16 TW If we found a way to extract this energy from Earth's rotation, how long would it take before the length of the day increased by 1 second?


Homework Answers

Answer #1

Work done = change in rotational kinetic energy,

W = (1/2)l(wf^2 - wi^2)

wi = 2*pi / T

wi = 2*pi / 86400 s = 7.2722*10-5 rad/s

When length of the day increased by 1 second,

wf =  2*pi / 86401 s = 7.2721*10-5 rad/s

I = (2/5)*MeRe^2 = (2/5)*5.97*1024*(6.37*106)2

I = 9.689*10^37 kg.m^2

Work done, W = (1/2) * 9.689*10^37 * ((7.2721*10-5)2 - (7.2722*10-5)2

W = 7.045*1024 J

P = W / t

t = W / P

t =  7.045*1024 / 16*1012

t = 4.403*10^11 s

t = 13965 yrs

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