The following seems an elementary geophysics query, but I’m not sure how to do a direct calculation. My geology text mentions that over the past 5 to 10 million years, the state of Utah and some adjacent states were uplifted about one mile, by tectonic forces. Part of this is the Colorado Uplift and is responsible for the Grand Canyon. So, I wondered just what minimal amount of energy might be required to do this work. To keep it simple, I imagined just the area of Utah, about 85,000 mi^2, converting it to sq meters: ~ 215 billion m^2. I also imagine this entire ‘block’ of rock is, say, 10 kilometers, or 10,000 meters deep. Again, for simplicity, I assume granite as a fair proxy for all kinds of rock in question. Granite weighs roughly 2,700 kg/m^3 . This suggests a rough total mass of: 2,700 kg/m^3 x 215 10^9 m^2 x 10,000 m, or about 5.8 10^18 kg. The uplift distance traveled is one mile or 1600 meters. The Earth’s gravitational acceleration “a” (=g) is about 9.8 m / s^2. So….
I’ve made a crude attempt to estimate the minimal energy required
by assuming it may equal force x distance traveled. ie:
Force x Distance = Mass * Acceleration * Distance, or
[5.810^18 kg] x [9.8 m/s^2] x [1600 m] = 9.1 X10^22 joules of energy.
(expended really over millions of years, by the way.)
But I don’t trust this estimate, since I suspect that there is a much
more elegant, accurate and direct solution available.
BTW, iff 9.110^22 joules were roughly correct, it would be the equivalent
of the energy coming from complete annihilation of about
1,011,000 kg of mass into energy. That is, the approximate energy
of one million hydrogen bombs. If true.
So is there a more accurate standard way of calculating the energy which
would be required?
Thanks,
Gene
