Question

How much energy could we get from flattening the Rocky Mountains? Guesstimate how much potential energy is stored in a mountain range.

Answer 1

Please note that this question has no specific or fixed answer. On planet earth, there are so many rocky mountains and ranges. So it depends which one we are considering.

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I will take The great Himalayan range as the example. The process will stay the same no matter what.

The highest peak as we all know is Mount Everest. The height of Everest is around 8848 m. As we need to take average height of whole range, its 8848 / 2 = 4424 m

The Himalayan range covers almost 2400 km (  India, Pakistan, Afghanistan, China, Bhutan and Nepal)

The width of the Himalayas from south to north varies between 200 and 400 km. We will take 400 km

volume of Himalayan range = 400 * 1000 * 2400 * 1000 * 4424 ( convert everything to meters)

volume of Himalayan range = 4.24e15 m³

Now, rock is much denser than water so, we will take density as 3000 kg / m³

therefore,

mass of of Himalayan range = 4.24e15 * 3000

mass of of Himalayan range = 1.274e19 Kg

now, to calculate potential energy, we need to use half of average height

P.E = mgh

P.E = 1.274e19 * 9.8 * 4424 / 2

P.E = 2.76e23 J

This is actually a good estimation.