Question 1090222
Given the Earth's radius of 4000 miles, and a mass of 200 pounds:
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The weight on the surface is 200 pounds.
What is the weight in an elevator to the Earth's center at various depths?
Depth of 500 miles, 1000 miles, 2000 miles, etc.
-\Ignore any effects of pressure and temperature.
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Inside a solid sphere of constant density, the gravitational force varies linearly with distance from the center, becoming zero by symmetry at the center of mass. This can be seen as follows: take a point within such a sphere, at a distance r from the center of the sphere. Then you can ignore all the shells of greater radius, according to the shell theorem. So, the remaining mass m is proportional to r^3, and the gravitational force exerted on it is proportional to m/r^2, so to r^3/r^2 = r, so it is linear in r.
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Weight = 200*(4000 - d)/4000 where d = the depth in miles.