# Why do conservative forces MUST depend on the position?

• svletana
In summary, conservative forces are defined as forces for which the work done along a closed path is zero. This means that they can either be constant, or depend only on position. Non-conservative forces, on the other hand, can depend on other variables such as time or velocity. The physical reason for this relationship is simply the definition of conservative forces. They are defined as such because their work is path independent, similar to how pi is defined as the ratio of the circumference of a circle to its diameter.
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?

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.

olgerm

## 1. Why do conservative forces depend on the position?

Conservative forces depend on the position because they are path-independent, meaning that the work done by the force on an object is only dependent on the initial and final positions of the object, not the path taken to get there.

## 2. What is the definition of a conservative force?

A conservative force is a type of force that does not dissipate energy and is dependent on the position of an object rather than its velocity. This means that the work done by the force is independent of the path taken by the object.

## 3. How do conservative forces relate to potential energy?

Conservative forces are related to potential energy because the work done by a conservative force can be expressed as the change in potential energy between two points. This means that as an object moves through a conservative force field, its potential energy is constantly changing.

## 4. Can conservative forces do work on an object without changing its kinetic energy?

Yes, conservative forces can do work on an object without changing its kinetic energy. This is because the work done by a conservative force is only dependent on the object's position, not its velocity. Therefore, the kinetic energy of the object remains constant even as work is done on it by the conservative force.

## 5. How do conservative forces differ from non-conservative forces?

Conservative forces differ from non-conservative forces in that they do not dissipate energy and are dependent on the position of an object rather than its velocity. Non-conservative forces, on the other hand, do dissipate energy and are dependent on both the position and velocity of an object.

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