Static friction

[uppi]

Thank you. It seems most others (merkin, uppi, souron) were missing Perf's point. It has nothing to do with experimental incertitude, Quantum Mechanics or this being a thought experiment.

Quantum mechanics is certainly involved here and needs to be considered: The forces between the atoms and molecules are quantum mechanical forces and have an uncertainity assiociated to it. Sum up the maximum of all these forces and you get the static friction coefficient, which should still have some uncertainity to it. Thus the "exact" coefficient of static friction is not defined, the only thing you can give are approximations.

If I say, let my "static coefficient of tallness" be my height, then this coefficient of tallness is exactly my height, BY DEFINITION. Sure I can't measure either it or my height exactly, yet they are still perfectly equal!

No, they're not: Your height changes over the day (I think it's around 0.5-2 cm). So a "coefficient of tallness" can not be defined more accurate than maybe 0.5 cm. It would be possible to measure the height accurate to 1 µm, but that would not make much sense, as that value would be wrong an hour later.

 

[LulThyme]

No, they're not: Your height changes over the day (I think it's around 0.5-2 cm). So a "coefficient of tallness" can not be defined more accurate than maybe 0.5 cm. It would be possible to measure the height accurate to 1 µm, but that would not make much sense, as that value would be wrong an hour later.

You seem to insist on missing the point. I'm not sure how to make it clearer.

My coefficient of tallness is exactly my height; that's how it's defined! They are equal, by definition.

If my height changes, then so does my coefficient of tallness. They are equal, by definition.

You are right that we cannot measure the coefficient of tallness (or my height) exactly. That doesn't change the fact that : they are equal, by definition.

 

[Souron]

EDIT: I gotta think some more on how to express myself.

 

[uppi]

You seem to insist on missing the point. I'm not sure how to make it clearer.

My coefficient of tallness is exactly my height; that's how it's defined! They are equal, by definition.

If my height changes, then so does my coefficient of tallness. They are equal, by definition.

You are right that we cannot measure the coefficient of tallness (or my height) exactly. That doesn't change the fact that : they are equal, by definition.

That would make your "coefficient of tallness" not a coefficient but a function of time. Your height as a function of time would indeed be equal to your height by definition. But coefficients are constant, so a coefficient of tallness would not be equal to your height by the definition of a coefficient, because your height is not constant.

Anyway, it's a different matter in the static friction coefficient. My point is, that it has an inherent uncertainity to it. That uncertainity is not related to measurement in any way, so even if we could exactly and perfectly measure it, it would still be not an exact value but a probabilistic distributed value.

 

[LulThyme]

Anyway, it's a different matter in the static friction coefficient. My point is, that it has an inherent uncertainity to it. That uncertainity is not related to measurement in any way, so even if we could exactly and perfectly measure it, it would still be not an exact value but a probabilistic distributed value.

It's no different. The coefficient of friction is DEFINED in terms of the force required to move the object. They are equal, by definition.

Your mantra since the start has been that there are obstacles to determining some values (whether because of measurement or other). This is true but irrelevant!

 

[uppi]

It's no different. The coefficient of friction is DEFINED in terms of the force required to move the object. They are equal, by definition.

Your mantra since the start has been that there are obstacles to determining some values (whether because of measurement or other). This is true but irrelevant!

You still didn't get the point: It's not that there are obstacles in determining these values, it's that these values do not exist that accurately. It's like the position of the electron in a hydrogen atom: You cannot give it accurate to 1 fm, because that value does not exist as the wavefunction is smeared out over 0.1 nm.

It's like saying that something is equal to the beard length of Santa Claus.

 

[Perfection]

Well there's practical exact, and then exact. For instance, in most of my classes we will lose points on graded work if we go out to more than three decimals. And we laugh at Mech E techs who will do work out to fifteen decimals because it's totally impracticle.

That's why I asked.

Well, from the classical standpoint you need absolute exactness in your force to get it on that coefficient otherwise it will be slightly above or below.

@uppi. so I was thinking what exactly would be the limits on the COF. Simple dimensional anaylsis doesn't give a clue, because the COF is dimensionless!

 

[uppi]

@uppi. so I was thinking what exactly would be the limits on the COF. Simple dimensional anaylsis doesn't give a clue, because the COF is dimensionless!

I think the limit should be rather given in terms of absolute friction force than in terms of the coefficient. But it would depend on many factors like size of the object, number fo atoms involved, type of material, surface structure and defects, temperature and so on. An absolute lower limit could be the binding force between two atoms, but this would again depend on the binding type. If we assume ~1eV for ionic bindings and a displacement of ~0.5nm (the magnitude of lattice constants) this would result in a force of ~10^-10N. However, I would expect that the limit kicks in much sooner, due to the other factors.