Is a Velocity Dependent Force Always Non-conservative?

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In summary, a conservative force is one that does not depend on velocity, meaning that changing the velocity will not change the work done on the same path. However, it is possible to have a force that depends on velocity, such as the magnetic force on a moving charge, which is still considered conservative because the work done on the particle is always zero. It is not known if there are any other forces with this property. To show that a velocity dependent force is not conservative, one would need to demonstrate that it has non-zero work on the particle.
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Gaudium
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Hi, I understand that a conservative force cannot depend on velocity, because by changing velocity we can do different work on the same path. But how can I show this mathematically, for a general force depending on velocity? Is the curl always zero for such a force?

Thank you?

Nese
 
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Are you sure about that? What about the force a magnetic field exerts on a moving charge?
 
  • #3
Yeah, you are right. As far as I know some people see the magnetic force as a conservative force although it depends on velocity, because the work done by it on a particle is always zero. I do not know any other force with this property. Maybe I have to reformulate the question as how do we show that a velocity dependent force is not conservative, which has nonzer work on the particle?
 

What are conservative forces?

Conservative forces are a type of force that does not dissipate energy and follows the law of conservation of energy. This means that the work done by conservative forces is path-independent, only dependent on the initial and final positions of an object.

What are some examples of conservative forces?

Examples of conservative forces include gravity, electric force, and magnetic force. These forces do not dissipate energy and their work depends only on the initial and final positions of an object.

How do conservative forces affect the motion of an object?

Conservative forces do not change the total mechanical energy of an object, but they can change the form of energy from potential to kinetic and vice versa. As a result, an object under the influence of conservative forces will oscillate between potential and kinetic energy.

Can conservative forces do work?

Yes, conservative forces can do work. However, this work is path-independent, meaning that the amount of work done by conservative forces only depends on the initial and final positions of an object, not the path taken.

How are conservative forces different from non-conservative forces?

The main difference between conservative and non-conservative forces is that non-conservative forces dissipate energy, while conservative forces do not. This means that non-conservative forces can change the total mechanical energy of an object, while conservative forces cannot.

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