1-dimensional non-conservative force that depends on position?

[Adoniram]

Homework Statement

Does there exist a 1-dimensional non-conservative force that depends on POSITION (not velocity)?

Homework Equations

N/A

The Attempt at a Solution

I've given this a lot of thought, and I can't come up with anything! Friction doesn't work, etc...

Any help would be greatly appreciated! :)

 

[berkeman]

Homework Statement

Does there exist a 1-dimensional non-conservative force that depends on POSITION (not velocity)?

Homework Equations

N/A

The Attempt at a Solution

I've given this a lot of thought, and I can't come up with anything! Friction doesn't work, etc...

Any help would be greatly appreciated! :)

Welcome to the PF.

Why doesn't friction work?

 

[rcgldr]

Would the hysteresis in a rubber band qualify it as a non-conservative?

 

[Adoniram]

Friction doesn't fit the definition because it is not dependent on position. Hysteresis... not sure. That seems more dependent on tension, but if it can be quantified in terms of position, that might work. What do you think?

 

[berkeman]

Friction doesn't fit the definition because it is not dependent on position. Hysteresis... not sure. That seems more dependent on tension, but if it can be quantified in terms of position, that might work. What do you think?

I think friction can work if you put one condition on it. Can you think of that condition?

 

[Adoniram]

I think friction can work if you put one condition on it. Can you think of that condition?

Are you referring to static vs kinetic? As far as I can tell, friction depends on some velocity being present (kinetic), or not present at all (static). As far as I can imagine, it doesn't depend on position, but I would love to hear which condition you refer to :)

 

[berkeman]

Are you referring to static vs kinetic? As far as I can tell, friction depends on some velocity being present (kinetic), or not present at all (static). As far as I can imagine, it doesn't depend on position, but I would love to hear which condition you refer to :)

We can't give out answers here at the PF (it's against the rules for schoolwork questions). So you will need to think on it more. I'm referring only to kinetic friction. Think about what you are trying to achieve in this problem, and see if you can think of what to do with friction to accomplish it...

 

[Adoniram]

Ok, so say you have a block sliding along a surface. The only way I can think of making the force of friction dependent on position is if the coefficient of friction changes along the surface. For example, if you have sand paper on the surface with changing grit values from left to right, then yes, the force of friction would absolutely depend on position.

I'm not sure if that's what my prof is going for, but I'll give it a whirl... I can't think of any others!

 

[berkeman]

Ok, so say you have a block sliding along a surface. The only way I can think of making the force of friction dependent on position is if the coefficient of friction changes along the surface. For example, if you have sand paper on the surface with changing grit values from left to right, then yes, the force of friction would absolutely depend on position.

I'm not sure if that's what my prof is going for, but I'll give it a whirl... I can't think of any others!

That's exactly what I was thinking of -- good for you for coming up with it! I think it satisfies the problem statement... The non-conservative force is position dependent, but not velocity dependent.

 

[Adoniram]

Thanks for your replies :)

The forum looks great, I don't know why I didn't find this earlier. I still have 1.5 more years of my degree program left, so this forum will undoubtedly be handy!