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The answer to all of the so called "energy flow" questions is buried in the
work/energy law/theorem.
None of the "energy" is "lost" but it doesn't "go" anywhere either. Work
is done on various parts of this complicated system by the various parts of
this system and the energy of these parts is increased or decreased, but
the energy does not move. Energy is a property of a system or its
parts. One would not likely say that blue moves. Blue paint can move, the
ball can move, but energy does not move by itself.