Line integral of friction forces

[marellasunny]

I was just performing the usual wine glass experiment where I rub my wet finger across the rim and I hear the resonant frequencies from the water column-due to the friction produced from my finger rubbing.
Today I learned about "conservative" forces from my professor.Since,frictional forces come under the category of non-conservative forces(which I gather means they depend on the path followed),shouldn't the sound produced by the water column vary upon the direction I choose to move my finger i.e C.W direction should produce one tone and A.C.W direction another tone??

1.But,practically,I get the same tone when I rub the finger in both clockwise and anti-clockwise directions.But,by the concept of non-conservative forces and [tex]\oint\!F.dr[/tex],shouldn't I get different tones for the C.W and the A.C.W directions?(since the work done by the frictional forces would vary for the diffferent paths I chose?)Maybe,resonance has something to explain for this,if so could you please elaborate?
2.Can I take the closed path integral for non-conservative forces?It seems illogical since there might be infinite points between many different paths.

Please help!Thanks.

 

[LightHero]

1. Yes, the concept of non-conservative forces and the closed path integral can explain why you get the same tone regardless of the direction you rub your finger in. This is because the frictional force is an oscillating force, meaning that it is constantly changing direction as you move your finger. This causes the work done by the frictional force to be equal in both directions, resulting in the same sound being produced regardless of the direction.2. No, you cannot take the closed path integral for non-conservative forces because there is no closed path for these forces. Non-conservative forces depend on the path followed, so there will never be a single closed path that captures all of the relevant information about the force. Instead, you must take into account the different paths taken and the different work done by the force along each of those paths.