Question

A satellite at a particular point along an elliptical orbit has a gravitational potential energy of 5100 MJ with respect to Earth's surface and a kinetic energy of 4200 MJ . Later in its orbit the satellite's potential energy is 5700 MJ . Part A Use conservation of energy to find its kinetic energy at that point.

Answer 1

To solve this problem we will apply the theorem given in the conservation of energy, by which we have that it is conserved and that in terms of potential and kinetic energy, in their initial moment they must be equal to the final potential and kinetic energy. This is,

$E_{initial} = E_{final}$

$PE_{initial}+KE_{initial} = PE_{final}+KE_{final}$

Replacing the 5100MJ for satellite as initial potential energy, 4200MJ for initial kinetic energy and 5700MJ for final potential energy we have that

$KE_{final} = (PE_{initial}+KE_{initial} )-PE_{final}$

$KE_{final} = (5100+4200)-5700$

$KE_{final} = 3600MJ$

Therefore the final kinetic energy is 3600MJ