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If one subdivides the spring into portions [...]
then one end moves farther than the other end
and so the equal and opposite forces at their two ends do not do equal and
opposite work, and each portion of the spring thus gains a portion of the
elastic PE.
From a sufficiently sophisticated point of view,it could be argued that we can have zero-sized
From the sophisticated point of view, expressing thelaws of motion in terms of "points" is not wrong.