Classical Mechanics, by John Taylor defines a conservative force F as a force that satisfies:
F depends only on the particle's position and no other variables.
Work done by F is the same for all paths taken between two points
I'm wondering if this definition is redundant. Doesn't (1) imply (2) and vice versa?
If not, what is an example of a force that satisfies (1) but not (2) and an example of a force that satisfies (2) but not (1)?