Why do conservative forces MUST depend on the position?

AI Thread Summary
Conservative forces are defined by their property that the work done along a closed path is zero, which means they can depend on position but do not have to. The discussion highlights that while a uniform force field is conservative, it does not depend on position. Non-conservative forces, on the other hand, typically depend on factors like time or velocity. The relationship between conservative forces and position dependence is nuanced, as some conservative forces may not vary with position. Understanding these distinctions is crucial for grasping the nature of forces in physics.
svletana
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...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?
 
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First off, you would be greatly served to use more precision when asking science questions. For example, when you say,

svletana said:
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.
 
svletana said:
...Or do they?
A uniform force field doesn't depend on position but is conservative.
 
svletana said:
...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.
 
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