Weight of Mountain
Name: Daniel M.
Date: February 9, 2004
How much does an average (as far as rock density is concerned and no volcanic activity) 10,000
foot tall mountain weigh?
Or at least...
How can you figure out the weigh of a mountain?
Interesting question. Find out what rock types are there and what their densities are
(you could even use an average density for granitic crustal material if you need to). I
think you could find the volume if you know area, height, and average slope of sides (calculus
would probably help you out here). Density is in g/cubic centimeters and you can find
volume in cubic centimeters, multiply the two and have your mass in grams, then convert to
kilograms. No matter what you do, the estimate will be very rough. I wonder if
geophysicists have already published papers relating to this?
A simple approximate way is to assume the density of rock is about 2.0gm/ml. You can choose
another density if you want. Assume the mountain is a cone and use the formula for the volume
of a cone to compute the total mass. Mountains are in fact "weighed" experimentally using
sensitive gravimeters -- instruments that measure the local gravitational constant. This is
done both on the ground and on satellites. From the variation of the local gravitational
constant the mass of the mountain can be determined by more sophisticated numerical
Typically, rock weighs roughly 2.7 as much as an equivalent volume of water. This would be
about 168 pounds per cubic foot or 2700 kilograms per cubic meter. But, what makes this
tricky is how you define the bottom of the mountain. The weight of the mountain deforms
the surrounding area, so how far down does it go?
To learn more about this process, search for information on the term "isostasy", which is the
theory of how the crust deforms under load.
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Update: June 2012