Question

What is the change in gravitational potential energy of 9.00- kg mass that is carried from the surface of the earth to a distance of one earth radius above the surface? Please show all work.

Answer 1

Since one fo the distances from the center of the earth is two times the radius of the earth we cannot take the aproximation

.

because that is only correct when the difference between the two heights is much smaller that the radius earth .

We have to take the gravitational force given by the universal gravitational law:

where

and

In our case

• m_e = 5.9736×10²⁴ kg the earth mass
• m_o = 9 kg
• r_a = R = 6.378×10⁶  m the radius of the earth
• r_b = 2×R = 12.756×10⁶ m two times the radius of the earth

To calculate the potential energy

Since the direction in the movement is oposite to the direction of the force

Repalcing the form of the gravitational force

Replacing the values

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