Conservative and non-conservative forces

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In summary, conservative forces conserve the total energy of an object while non-conservative forces do not. Conservative forces involve no net work and are path-independent, while non-conservative forces require work to be done and are path-dependent. Potential energy can only be defined for conservative forces and is dependent on the starting and ending points, while the force itself must be conservative.
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JasonAdams
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Can somebody please help me understand conservative and non-conservative forces? My teacher didn't really spend too much time teaching it. Can somebody explain it in the simplest terms possible?
 
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  • #2
JasonAdams said:
Can somebody please help me understand conservative and non-conservative forces? My teacher didn't really spend too much time teaching it. Can somebody explain it in the simplest terms possible?

http://en.wikipedia.org/wiki/Conservative_force
 
  • #3
"Conservative" forces conserve the total energy of an object and non-conservative forces don't! That, at any rate, is where the name comes from. Since total energy of an object is the sum of kinetic energy (depending only on speed) and potential energy (depending only on position), if you move an object around with only conservative forces involved, finally returning it to its orignal position and original speed, you have not changed the total energy and so have done no net work. Gravity is an example of a conservative force. The force moving planets around the sun returns then, eventually, to the same point in their orbit with the same speed and so does no net work. That's why gravity doesn't "run out"!

Friction, on the other hand, is a non-conservative force. If you move a refrigerator across the kitchen you are not changing its height and so not its potential energy. If after moving it across the room and leaving it standing still you have not changed its total energy. But you certainly will have to do work! You have to do work to overcome friction- that work goes not into the energy of the refrigerator but causes the floor to be slightly warmer.
 
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  • #4
In addition, the potential energy can only be defined for the (minus) work of a conservative force. The key is that the work depends ONLY on the starting and ending points, and not on the trajectory. Otherwise (for a non-conservative force) the path has to be specified, so it makes no sense to speak of a potential energy which should depend only on the position.

The path-independence of the work is equivalent to saying that the net work (due to that conservative force) in any closed path is zero.
 
  • #5
Thanks for the help.
 
  • #6
xnick said:
In addition, the potential energy can only be defined for the (minus) work of a conservative force.

Isn't that just a convention?
 
  • #7
neutrino said:
Isn't that just a convention?

I guess the sign is conventional (although i don't think anyone's going to change it now) and also you can add an arbitrary constant to the potential energy and get the same physical results, since the quantities of interest are energy differences.

But the force MUST be conservative.
 
  • #8
Conservative - point dependent
Non-conservative - path dependent
 

1. What is the difference between conservative and non-conservative forces?

Conservative forces are those that do not dissipate energy and can be defined by a potential energy function, while non-conservative forces are those that dissipate energy and cannot be defined by a potential energy function.

2. What are some examples of conservative and non-conservative forces?

Examples of conservative forces include gravity, electric forces, and magnetic forces. Examples of non-conservative forces include friction, air resistance, and tension in a rope.

3. How do conservative and non-conservative forces affect an object's motion?

Conservative forces do not change the total mechanical energy of an object, but can change its potential and kinetic energy. Non-conservative forces, on the other hand, can decrease the total mechanical energy of an object by doing work against it.

4. Can a force be both conservative and non-conservative?

No, a force can only be either conservative or non-conservative. A force cannot dissipate energy and have a potential energy function at the same time.

5. How can we determine if a force is conservative or non-conservative?

A force is conservative if it meets two criteria: 1) it does not depend on the path taken by the object, only on the initial and final positions, and 2) the work done by the force is independent of the path taken. If a force does not meet these criteria, it is non-conservative.

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