Question

A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight. (a) Calculate the mass of the mountain. (b) Compare the mountain’s mass with that of Earth. (c) What is unreasonable about these results? (d) Which premises are unreasonable or inconsistent?

Answer 1

Answer:

a)   M = 2,939  10¹⁷ kg , b)   $M_{e}$ / M  = 2 10⁷

Explanation:

a) The equation for gravitational force is

         F = G m M / r²

Where G is the gravitational constant that is worth 6.67 10⁻¹¹ N m² / kg², m the mass epa person. M the mass of the Mountain and r the distance between them.

The value of this force is 2% of the person's weight

          F = 0.02 W = 0.02 mg

we replace

         0.02 mg = G m M / r²

         M = 0.02 g r² / G

         r = 10 km = 10 10³ m = 1.0 10⁴ m

         M = 0.02  9.8  (10⁴)² / 6.67 10⁻¹¹

         M = 2,939  10¹⁷ kg

b) to compare the masses we find their relationship

       $M_{e}$ / M = 5.98 1024 / 2,939 1017

       $M_{e}$ / M  = 2 10⁷

c) treating the mountain as a point object

d) The mountain is not spherical so the distance changes depending on the height of the mountain