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I think, say in an elastic collision perpendicular to Fg, W=ΔK could be used to find the amount of work done on the ball if it hits something. By Newton's third law, the force on the ball will equal the force on the object it is colliding with, and while they are exerting a push on eachother they will be in contact and therefore will move together. So the work done on the object by the ball=the negative of the work done on the ball by the object=-ΔK of the ball. Therefore the amount of kinetic energy that was lost by the ball can be said to have been used to do work on the object. right? So I can kind of see where a relationship such as the one my professor described might be seen as possible at first, but after some investigation I cannot see how what he said can be true.

Also, I remember him insinuating that the declining potential energy of a falling ball=increasing potential energy of the earth. But that makes absolutely no sense to me, as the ball's potential energy is being converted into kinetic energy. Even if I view the earth as falling towards the ball, the earth's capacity to do work due to its position in the ball's gravitational field is being turned into kinetic energy of the earth as they come closer together. I cannot see how in the world it would increase.

Please help! If I can just either know that he is wrong, or see mathematically that the work on the ball by the earth =the work on the earth by the ball, I can rest easy.