Static friction

[Globex]

Lets say there's an object on a table with friction. If you apply a force on the object that exactly equals the force of static friction, what will happen to it?

My physics teacher says the object will start to move but if the force you apply is exactly equal to the force of static friction, isn't the net force on the object zero?

 

[uppi]

Classically, you're right. If the net force is always zero it won't move. However, this is a very unstable state, once it starts moving, the friction will decrease and it will keep accelerating. If you keep it exactly at the balance point, then a very tiny force in the right direction will cause it to move. And there are always enough fluctuations, that such a force is almost certain to happen.

So your teacher is right. You will not be able to keep the object in that unstable state, so it will start moving.

 

[Perfection]

When ever you push on an object on a level table and it doesn't move the force you apply is exactly equal to the force of static friction.

 

[Veritass]

Not completely on topic, but I remember seeing a demonstration once with a simple device where the guy hooked up a hand winch (like you would use on a boat trailer) with about a four-foot elastic (bungie) cord to a large brick on a flat surface. He would then crank the winch in an even motion, putting more and more tension on the cord, until the brick would finally slide forward and come to a stop in a new location.

He repeated this several times, and then made the following observations:
- We cannot ever be certain exactly when the brick will move.
- The longer we wait for the brick to move, the more force is built up, and the farther the brick will move.

This is exactly what happens in an earthquake fault such as in California. We cannot ever be certain when the force will build up enough to move, but the longer we wait, the larger the earthquake will be.

I just thought it was a simple and effective demonstration of this.

 

[ParadigmShifter]

Well friction is chaotic and you can't measure exactly the coefficient of friction for a particular instance of brick on table. We just have "rough" (excuse the pun) guidelines for various material vs. material coefficients.

Exactly equalling the force of friction places the system in an unstable equilibrium I presume.

 

[Perfection]

Another issue that needs to be addressed is plausibility of getting the exact amount of a specific force. How do you get an exact real value?

The probability of exerting the exact force seems to me to be zero. (at least by classical continuum mechanics)

 

[ParadigmShifter]

Yeah, hence it is a chaotic system.

 

[SS-18 ICBM]

I'd say if it's equal it starts moving at constant velocity. Anything beyond that would be acceleration.

 

[Perfection]

Yeah, hence it is a chaotic system.

It doesn't seem especially chaotic to me, we could very well produce a setup with much more reliable friction coefficients that are repeatable to an arbitrary amount of precision (instead of brick on rough wooden table, we use very carefully machined aluminum plate on a robot-sanded ultra smooth surface steel table or something). My objection is not that you need to exactly measure a coefficient of friction. Rather, that you need to exactly measure something. The probability of getting a specific real number out any continuous probability distribution is exactly zero. You can get arbitrarily close to exact, but you aren't gonna get exact.

I'd say if it's equal it starts moving at constant velocity. Anything beyond that would be acceleration.

That is most clearly not the case. When an object is moving moving it is subject to the coefficient of kinetic friction, not static friction. The coefficient of kinetic friction is lower.

 

[SS-18 ICBM]

Right, forgot about that...

 

[Merkinball]

Another issue that needs to be addressed is plausibility of getting the exact amount of a specific force. How do you get an exact real value? - Perfy

How exact is exact? How many sig figs are you looking for? If I wanted it to be exact I'd rig up something hydraulic on a load cell, then collect data off of the load cell. You can get cheap load cells with .05% accuracy relatively cheap.

 

[Atlas14]

How exact is exact? How many sig figs are you looking for? If I wanted it to be exact I'd rig up something hydraulic on a load cell, then collect data off of the load cell. You can get cheap load cells with .05% accuracy relatively cheap.

That is pretty terrible accuracy...

 

[Perfection]

How exact is exact?

Perfectly exact, not approximately exact.

 

[Merkinball]

That is pretty terrible accuracy...

Wut? If you have a 20lb force that is required to move it you can program your load cell to stop actuation between a hundredth of a pound. That's not terrible accuracy.

Perfectly exact, not approximately exact. - Perfy

Alright, if you say so. Can't be done.

 

[Perfection]

Alright, if you say so. Can't be done.

Sorta my point.

 

[Merkinball]

Sorta my point.

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.

 

[uppi]

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.

15 decimals can be practical and even needed in certain cases. How much exactness is practical is only determined by your need and your equipment. In our lab we can control frequencies with an accuracy better than 10^-9 and we're not even trying that hard.

In this case exact would be determined by how accurate the maximum friction is actually defined. The maximum friction will have some uncertainity to it (I suspect it is actually very broad), and if the control of the force is better than that, there is no point in increasing it any further.

 

[Souron]

15 decimals can be practical and even needed in certain cases. How much exactness is practical is only determined by your need and your equipment. In our lab we can control frequencies with an accuracy better than 10^-9 and we're not even trying that hard.

9 sig figs for the frequency of light seems high to me. What frequency is it around?

In this case exact would be determined by how accurate the maximum friction is actually defined. The maximum friction will have some uncertainity to it (I suspect it is actually very broad), and if the control of the force is better than that, there is no point in increasing it any further.

This is a gedanken experiment, the coefficient of friction can be defined exactly.

 

[uppi]

9 sig figs for the frequency of light seems high to me. What frequency is it around?

Around 380 THz (near IR)

This is a gedanken experiment, the coefficient of friction can be defined exactly.

In that case we can also exactly set the force, so the question of accuracy doesn't appear. However I'd say, that quantum mechanical uncertainity would ensure that the maximum friction becomes probabilistic at one point (i.e. a certain probability to start moving at a certain applied force), so defining an exact coefficient of friction might not make much sense.

 

[LulThyme]

Hello,
Static frictional forces from the interlocking of the irregularities of two surfaces will increase to prevent any relative motion up until some limit where motion occurs. It is that threshold of motion which is characterized by the coefficient of static friction.

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.

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!