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You are correct, Bob, for a single particle MODEL. But the reality of the
situation is more complicated. Two internal non-conservative forces are
involved in a process by which internal kinetic energy K (macroscopic)
is converted into thermal energy (microscopic). And if my understanding
of Bruce Sherwood is correct (his AJP article was mentioned here) it is
not at all obvious what fraction of the really-observed x should be used
to calculate the work correctly.
Ludwik Kowalski