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In trying to convince myself that the total potential energy of a system of two particles was just the potential energy of one particle computed while considering the other particle fixed, I imagined two identical particles a distance 2r apart and attracting each other, and concluded that their total kinetic energy when they meet would be the same if both particles were free as if one was fixed.

But I don't know how to prove the thing in the most general case possible. Can anyone help?

Thanks.

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# Potential energy of a system of particles

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