# Conservative force definition

Classical Mechanics, by John Taylor defines a conservative force F as a force that satisfies:

1. F depends only on the particle's position and no other variables.

2. 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)?

• What if the force is dependent only on the particle's position and on time? – probably_someone Feb 11 '18 at 20:23