Conservative force a question?

Question

i know that work that's done on an object in a closed path equals zero if the field is conservative.

but is it if and only if ?

i mean, is it possible for the work to be zero (on a close path) if the field is not conservative ?

thanks !

Answer 1

This is a very important question and one that you will encounter in many different aspects of physics.

Work done on an object in a closed path is zero if and only if the force is conservative.  if the force is non-conservative, then it is not possible for the work to be zero.

If you have studied vector calculus, read up on the curl of a vector field (and the test for a conservative force is that its curl is zero) and Stokes' Theorem.

hope this helps