Because I fear that we are losing the forest for the trees in this thread,
I'd like to remind everyone that the question, "How much work is done?" is
not at *all* interesting--as Leigh might say, it could form the basis for
a multiple choice question but it is devoid of inherent utility. There is
no way to make a "mistake" (beyond the usual trivial mathematical ones) in
calculating work because the answer depends on the definition being
employed.
The answer to the question, "How much work is done?" *becomes* useful only
when one can use it to do physics. One can only do *that* through the use
of work-energy relationships. Here one can (and in my experience far too
often does) make mistakes.
My crusade is to see fewer mistakes made in the use of work-energy
relationships, NOT in the calculation of work.