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When you correctly use a work-energy theorem (validly derived from
newton's laws) to calculate a numerical quantity you are on the
solid ground of a mathematical model - a testable numerical equality.
When you interpret these numerical results in terms of "particular energy
losses, gains, transfers, transformations, etc among particular objects",
you are in the completely different realm of a conceptual model - a shaky
ground of subjective taste based on metaphorical associations with everyday
real and imagined human experience.
You can do your students no greater service than to emphasize this
distinction when you explain "How you know".
In general work done against a conservative force
BECOMES POTENTIAL ENERGY ASSOCIATED WITH THAT FORCE
(energy=ability to do work).