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Why is Mauna Kea taller than the maximum height possible on Earth?

Earth Science Asked by Aneek on February 2, 2021

We can calculate the maximum possible height of the mountain on earth.
If the elastic limit of a typical rock is $3 times 10^8 mathrm{N/m}$ and its mean density is $3 times 10^3 mathrm{kg/m^3}$, then the breaking stress is $h,rho,mathrm{g}$, where $h$ is height, $rho$ is the density of the rock, and $mathrm{g}$ is the acceleration due to gravity. Then

$$ h = frac{mathrm{elastic limit}}{rho,mathrm{g}} $$

Putting the values we get,

$$ h = 10^4 mathrm{m} $$

which is the maximum possible height. Now Mount Everest is within this limit, but Mauna Kea is 10,210 m tall (measured from its oceanic base).

Does this suggest that rock types at the base of this mountain are different?
Or does the presence of water have an effect?

3 Answers

Since over half of the height of Mauna Kea is under water, you need to consider the buoyancy effect. Instead of a density of $3 times 10^3 mathrm{kg/m^3}$, the underwater portion has a net density of $2 times 10^3 mathrm{kg/m^3}$. That will significantly increase the potential height of such a mountain. Add in all the other uncertainties (is Mauna Kea made of rock with "typical" elastic limit and density? is it even homogenous? are there dynamics involved? and what about Naomi?) and there's no reason to see its height as a contradiction.

Answered by Daniel Griscom on February 2, 2021

Your calculation of maximum height has a precision of one significant figure, 10000 meters. That is consistent with the height of Mauna Kea to the same precision of one significant figure. The difference, 210 meters, doesn't matter. Your question doesn't really make sense the way you have stated it.

You need to propose a model, and do a calculation, having more precision. Your estimate of the maximum height needs more significant figures in it before you can say whether it is or is not consistent with observation.

The stress below Oceanic Islands, such as the Hawaiian Islands, does exceed the strength of the crust and upper mantle. When volcanism ceases, oceanic islands sink below sea level.

Answered by Mark Rovetta on February 2, 2021

Basaltic rock is denser than granitic rock and that makes the difference. Also since 2/3 of the mountain is underwater thousands of feet of water are pressing against it to take yield of it's weight. it's like a 300 lb man, jumps in the pool, takes enormous weight pressure off.

Answered by LazyReader on February 2, 2021

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