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... when somebody talks about "potential energy", what comes
to my mind is the definition of potential energy.
(To avoid subscripts, allow me to write U instead of PE.)
What is U, then? I was thaught that
"The so called potential energy, is a scalar function U(x,y,z)
that has the following property: grad U = - force." (eq 1)
If we agree that this is a good definition of potencial
energy, then it follows that
Delta W = - grad U dot ds (eq 2)
As you see, it will be very difficult to isolate the
analysis of the notion of potential energy and the notion of work.