If an object were 10.0 meters above the surface of the moon, how would its potential energy compare when the same object is 10.0 m above the surface of the eart

Question

  If an object were 10.0 meters above the surface of the moon, how would its potential energy compare when the same object is 10.0 m above the surface of the earth?

Answer 1

Look up in your science book the acceleration of gravity on the surface of the moon.  Call it g'.  On the surface of the earth, 

 

g = 9.8 m/s²

 

Gravitational potential energy above the surface of the earth is 

 

U = mgh

 

Gravitational potential energy above the surface of the moon is

U' = mg'h

 

⇒

 

U'/U = (mg'h)/(mgh) = g'/g

 

This shows the gravitational potential energy above the surface of the moon is the fraction g'/g times the gravitational potential energy above the surface of the earth.  Look up g' in units of m/s², compute g'/(9.8 m/s²), and you will have your answer.