Why do conservative forces MUST depend on the position?

[svletana]

...Or do they? I read on a book a few years ago that you can spot a conservative force seeing if it depends on the position or not. That means a non conservative force doesn't depend on the position. What is the physical reason for the relationship between a force being conservative and the function depending on the position?

 

[mfig]

First off, you would be greatly served to use more precision when asking science questions. For example, when you say,

What is the physical reason for the relationship between a force being conservative and the function depending on the position?

What "the function" are you talking about? "The function" could be a lot of things. Be specific.

Are you talking about the work done by a conservative force being path independent? If so, then you are referring to a definition of conservative forces. It is akin to asking, "Why is pi the ratio of the circumference of a circle to its diameter?" Pi is defined as this ratio; that is why it is this ratio! Similarly, a conservative force just is a force for which the work done along a closed path is zero. That is what the term means.

 

[A.T.]

...Or do they?

A uniform force field doesn't depend on position but is conservative.

 

[ehild]

...Or do they? I read on a book a few years ago that you can spot a conservative force seeing if it depends on the position or not. That means a non conservative force doesn't depend on the position. What is the physical reason for the relationship between a force being conservative and the function depending on the position?

No, conservative forces need not depend on position, but they can depend only on position. A constant force is conservative.
A force dependent on time or velocity is not conservative.