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doesn't depend on how you got from A to B.
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Even more interesting is that
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all the fundamental forces that we know --
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gravity, electrostatics,
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even the strong force, weak force,
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every force that we know to the extent it can be described by a force --
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happens to be conservative.
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So, it's not that we are hung up
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on some rather exceptional case;
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nature is kind enough that
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all the forces are conservative.
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Now, friction is a little tricky.