Limit of a mountain using universal gravitation

In summary, the height of a mountain is determined by the ability of the atoms at the bottom to support the weight of the materials above them. Given that the tallest mountains on Earth are close to this limit at about 8850m, the maximum height of a mountain on Mars can be calculated using the equation F=G(m1*m2/R^2). The mass and radius of Mars (.11Me and .53 Re, respectively) can be used to find the value of g on the surface of Mars, which can then be used in the equation to determine the maximum height of a mountain on Mars.
  • #1
BoldKnight399
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The height of a mountain is limited by the ability of the atoms at the bottom to sustain the weight of the materials above them. Assuming that the tallest mountains on Earth (at about 8850m) are near this limit, how tall could that mountain be on Mars, with mass .11Me and radius .53 Re?

I know that this should include the equation:
F=G(m1*m2/R^2) but I don't understand how. To be honest I don't understand how one could possibly find an actual number from this limited information. (it is a multiple choice answer question, and all the choices are numbers. However, I would rather solve it myself so I can understand the concept.)
 
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  • #2
Hint: what would the value of g be on the surface of Mars?
 

1. What is the limit of a mountain using universal gravitation?

The limit of a mountain using universal gravitation refers to the maximum height that a mountain can reach before being crushed by its own weight due to the force of gravity. This limit is determined by the strength of the mountain's materials and the pull of gravity.

2. How is the limit of a mountain calculated using universal gravitation?

The limit of a mountain can be calculated using the formula F = GmM/r^2, where F is the force of gravity, G is the gravitational constant, m and M are the masses of the mountain and the Earth, and r is the radius of the mountain.

3. Can the limit of a mountain change over time?

Yes, the limit of a mountain can change over time as the materials of the mountain erode or the Earth's mass and radius change. This is a gradual process and can take thousands or even millions of years.

4. How does the limit of a mountain using universal gravitation relate to its height?

The limit of a mountain is directly related to its height. As the height of a mountain increases, so does the force of gravity acting on it. If the mountain's height exceeds its limit, it will collapse under its own weight.

5. Are there any mountains that have reached their limit using universal gravitation?

Yes, there are mountains that have reached their limit using universal gravitation, such as Mount Everest. However, the limit is constantly changing due to erosion and other geological processes.

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