Is a Velocity Dependent Force Always Non-conservative?

[Gaudium]

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

 

[vela]

Are you sure about that? What about the force a magnetic field exerts on a moving charge?

 

[Gaudium]

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?