Conservation of energy in a moving frame

[Electric to be]

I know a similar question has been asked but I'm still kind of stumped.

Imagine the Earth on the left and a small mass to it's right separated by some distance h.

You are in the frame of reference where the Earth and the small mass are moving to your right at some speed v.

So, both the Earth and the ball have some initial kinetic energy (1/2)(respective mass)v^2 and the ball Earth system will lose a potential energy of mgh as they come together.

So the Earth won't gain any significant energy since it is so massive but the ball appear to lose energy since it is accelerated to the left. How is energy conserved if the potential energy is gone and the ball Earth system appears to actually lose energy?

My only possible reasoning is that potential energy is somehow relative? But the equation for total potential energy being equal to -GMm/r makes it seem pretty absolute (in a non relativistic setting of course)..

Thank you for any help!

 

[RaulTheUCSCSlug]

A bit confused from your wording, but you must keep in mind that with collisions and a moving frame of reference it might appear that energy is not conserved. For that reason, one does not usually use a moving frame unless it makes the calculations easier for what you need. But when having to use conservation of energy as a total, the whole frame must always be considered because there is no actual energy lost. Even if it is lost through friction the energy must be accounted for.

 

[RaulTheUCSCSlug]

Potential energy between two bodies of mass is going to be relative to the mass of both objects. The force one feels on the other will be the same, so I am unsure on what you mean by absolute? The constant between two bodies is going to always be G with all other variables being able to be changed given different circumstances. (although usually mass is thought of as constant)

Also in the situation you gave, the energy gained may not be significant compared to that of the Earth but is going to be the same from the small ball. Why would they be different?

 

[jbriggs444]

So the Earth won't gain any significant energy since it is so massive but the ball appear to lose energy since it is accelerated to the left.

Your intuitition is telling you that the Earth won't gain any significant energy. Your reasoning is telling you that this doesn't make sense.

Why don't you test your intuition? How much kinetic energy does the Earth gain? How much kinetic energy does the ball lose? Do the calculated results match your intuition?