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But I also explain to my students there is a big sign problem when we try
use the "work-energy theorem" because the work-energy theorem itself doesto
not specify whether the agent doing the work done and the thing changing
energy are the same. So, when I write the work-energy theorem I simply
write W = +/- delta-E and tell the students they have to figure out which
sign is appropriate on a case-by-case basis.
Conclusion, I believe there is a firm sign convention for what I consider
the formal definition of work (integral force dot ds). But there is no
formal convention for the sign used in the work-energy theorem because the
theorem does not specify whether both sides of the equation are referring
the same body/agent or not.