Why do conservative forces MUST depend on the position?

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Discussion Overview

The discussion centers around the relationship between conservative forces and their dependence on position. Participants explore the definitions and characteristics of conservative and non-conservative forces, questioning the physical reasoning behind these relationships. The scope includes conceptual clarifications and technical explanations related to force definitions in physics.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that a conservative force is defined by its work being path independent and that this definition does not inherently require a dependence on position.
  • Others argue that while conservative forces can depend on position, they do not necessarily have to, citing examples like uniform force fields that are conservative yet position-independent.
  • A participant emphasizes the need for precision in discussing the definitions and relationships of forces, questioning what is meant by "the function" in the context of conservative forces.
  • It is noted that a constant force is an example of a conservative force that does not depend on position, while forces that depend on time or velocity are categorized as non-conservative.

Areas of Agreement / Disagreement

Participants express differing views on whether conservative forces must depend on position, with no consensus reached on this aspect of the discussion.

Contextual Notes

Participants highlight the importance of precise definitions and the potential for misunderstanding when discussing the characteristics of forces. The discussion reveals ambiguities in the definitions and examples provided.

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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