Friction - why not conservative force?

[enippeas]

We know that friction caused by electromagnetic forces. But then, why friction isn't a conservative force?

 

[gabbagabbahey]

Electrostatic forces are conservative, but Electromagnetic forces, in general, are not.

 

[Andrew Mason]

Electrostatic forces are conservative, but Electromagnetic forces, in general, are not.

I don't quite understand why you say electromagnetic forces are not conservative. With time-dependent electric or magnetic fields, some electromagnetic energy is radiated away (a very small amount) and is, therefore, not conserved within the system. But that does not explain friction losses. Very little of the energy lost due to friction is due to radiation losses.

Friction losses are due to the fact that the work done against friction results in heat. The laws of thermodynamics put significant limitations on the amount of work that can be obtained from heat energy. Most of that heat energy cannot be recovered in a form that is useful (ie. that can be converted to work).

AM

 

[Andy Resnick]

We know that friction caused by electromagnetic forces. But then, why friction isn't a conservative force?

We don't have a microscopic theory of friction; it's currently impossible to say what the cause of friction is.

You are correct- friction is a dissipative process even though the electromagnetic force is not. Nobody knows why.

 

[Andrew Mason]

We don't have a microscopic theory of friction; it's currently impossible to say what the cause of friction is.

We may not have a perfectly complete theory of friction because it is complicated and occurs in different ways (surface-surface sliding, rolling friction, viscosity, gas/fluid flow etc). But that does not mean that it impossible to say what it is. Generally, it is the result of microscopic interactions between matter in relative motion. We know that matter interacts through electro-magnetic forces. We know that these interactions generate heat, which is random molecular motion. So we know that friction causes molecules to move faster.

You are correct- friction is a dissipative process even though the electromagnetic force is not. Nobody knows why.

The fact that the actual mechanism is not completely known does not mean that nobody knows why friction is a dissipative process.

The reason it is a dissipative process is because it produces heat. Useful energy (ie energy that can do work) cannot be fully recovered from heat. Forces that do work producing heat (which is a purely macroscopic phenomenon) cannot be conservative due to the laws of thermodynamics (which apply only to macroscopic phenomena).

Low entropy kinetic energy of macroscopic objects is converted to high entropy kinetic energy of molecules. But the high entropy kinetic energy of those molecules cannot be used to restore the original low entropy kinetic energy of the macroscopic objects. That would violate the second law of thermodynamics. That is why it is dissipative.AM

 

[Andy Resnick]

But that does not mean that it impossible to say what it is.
<snip>

The fact that the actual mechanism is not completely known does not mean that nobody knows why friction is a dissipative process.

<snip>

AM

I don't want to get into a quibble battle over the meanings of 'cause' and 'why'. I will simply point out I did not say 'we do not know what friction is'.

 

[enippeas]

I think the crucial point is that the system sliding mass - surface is not a closed ( by energy) system despite the fact that electromagnetic forces are in general non-conservative. The kinetic energy flows from molecule to molecule and the system cannot retain his energy.

 

[Andy Resnick]

It's true that there is a diffusion-type flow of energy: dissipative processes seem to require the interaction between a system of interest and a heat bath. I'm not very familiar with current models, but Dattagupta and Puri's "Dissipative Phenomena in Condensed Matter" has several chapters on classical systems in addition to several chapters on quantum dissipative systems.

As best I can tell, the starting point is a Langevin-type equation:

$$\frac{dP}{dt}= -\frac{\partial U(Q)}{\partial Q}-\int dt' \frac{P(t')}{M}\varsigma (t-t') + \theta (t)$$

Where P, Q are the particle momentum and position, etc.

The term $\varsigma (t-t')$ is a friction-type term, written as a memory function- it reduces to Ohmic dissipation in the limit of a large number of oscillators in equilibrium with a heat bath (and some other simplifications), leading to :

$$\varsigma_{0} = \frac{3 \pi C^{2}}{2m\omega^{3}_{c}}$$

see also:
http://www.physics.arizona.edu/~cronin/Research/Lab/some%20decoherence%20refs/GAL93.pdf

 

[K^2]

We know that friction caused by electromagnetic forces. But then, why friction isn't a conservative force?

If you consider motion of every single particle in the entire system, friction is conservative, and so is every other force involved. It's also a total mess, because it is simply impossible to track motion of enough particles to build any kind of a useful model.

For that reason, physics usually breaks down the system into macroscopic bodies, each of which consists of a huge number of particles. We consider motion of the center of mass to be contribution to mechanical energy, while motion of individual particles as part of internal energy. Since internal energy, in general, cannot be recovered completely, and in most systems we consider we do not even try to, this energy is considered to be lost. Consequently, the force that converts mechanical work into heat is resulting in loss of mechanical energy, and is therefore non-conservative.

Does that help?

P.S. It doesn't really matter what the mechanism of friction is. All known fundamental forces are conservative. Pretty much the entire foundation of physics rests on that fact. So whatever forces we do break up friction into, they will ultimately be conservative.

 

[Andy Resnick]

It's also a total mess, because it is simply impossible to track motion of enough particles to build any kind of a useful model.
<snip>

So whatever forces we do break up friction into, they will ultimately be conservative.

I really don't understand this viewpoint. It's fine to say you are not interested by the problem, but to simultaneously claim it is solved while also stating it's impossible to model strikes me as defeatist- or claims the problem as beyond the reach of science.

Never mind that it insults all the people doing research into the origin of dissipation.

If we understood dissipation, as "understood" is commonly meant, we would be able to design materials with an arbitrary coefficient of friction- or fluids with arbitrary viscosity. Or materials with an arbitrary conductivity. Or have quantum computation. Or understand the glass transition. We can't do any of these things because we don't understand dissipation and how it arises from underlying conservative forces.

As an analogy, while we have a very accurate model for a hydrogen atom, we have not solved the problems of materials science, chemistry, or biology.

 

[K^2]

I never said it's impossible to model dissipation. There are plenty of models in plenty of branches of physics. There are some really nice models for dissipation in solid state, for example. It's impossible to build a fully reversible model, which would retain conservative nature of fundamental forces. You have to resort to statistical methods, and that's what leads to non-conservative forces in the first place.

 

[quantum1423]

I think that friction is electrostatic interactions at a very small scale. Electrostatic interactions are conservative, but tons of them aren't if you treat it as a whole. For example, in a whole pool of positive charges like this:
+++++++++++++++++++++++++++++++++++
a "grid" of positive ions laid flat on the X-Y plane. True, the force is conservative in the X-Z and Y-Z plane, but for a positively charged ball hovering in the X-Y plane parallel to the grid, the force is NOT conservative: a test charge quickly shooting across the grid will have not NEARLY as much work done on it as a test charge sitting right on top of the grid. Friction is much the same thing: a whole pool of electrostatic forces VIEWED AS ONE FORCE is not conservative.

 

[Andy Resnick]

I never said it's impossible to model dissipation.

Actually, as a point of fact, you did:

If you consider motion of every single particle in the entire system, friction is conservative, and so is every other force involved. It's also a total mess, because it is simply impossible to track motion of enough particles to build any kind of a useful model.

For that reason, physics usually breaks down the system into macroscopic bodies, each of which consists of a huge number of particles. We consider motion of the center of mass to be contribution to mechanical energy, while motion of individual particles as part of internal energy. Since internal energy, in general, cannot be recovered completely, and in most systems we consider we do not even try to, this energy is considered to be lost. Consequently, the force that converts mechanical work into heat is resulting in loss of mechanical energy, and is therefore non-conservative.

Does that help?

P.S. It doesn't really matter what the mechanism of friction is. All known fundamental forces are conservative. Pretty much the entire foundation of physics rests on that fact. So whatever forces we do break up friction into, they will ultimately be conservative.

 

[K^2]

If you consider of motion of every single particle, it IS impossible to build a useful model. All of the useful models don't bother with motion of individual particles. They bother with properties of a statistical average particle.

Why don't you read a whole sentence rather than get stuck on a phrase? Or are you simply not familiar with statistical mechanics?

 

[Andrew Mason]

I understand where Andy is coming from but I don't think the OP requires that much of an answer. There is a well developed science of thermodynamics that does not require a model for, or deep understanding of, what is happening at the molecular or sub atomic level. The second law of thermodynamics explains completely why friction is not a conservative force.

AM

 

[Andy Resnick]

The second law of thermodynamics explains completely why friction is not a conservative force.

AM

I agree with this, definitely.

 

[Andy Resnick]

If you consider of motion of every single particle, it IS impossible to build a useful model. All of the useful models don't bother with motion of individual particles. They bother with properties of a statistical average particle.

Why don't you read a whole sentence rather than get stuck on a phrase? Or are you simply not familiar with statistical mechanics?

I've never claimed to be an expert in SM. I only pointed out an error.

I would like to know more about what you call 'useful models' - I am only familiar with ones based on Langevin/Fokker-Planck/Smoluchowski type equations, which are transformed into the fluctuation-dissipation relation. The models I mentioned in Post #8 were very confusing (to me) and I don't understand them very well.

 

[K^2]

There is no error. My original statement is sound as stated.

 

[marcusl]

Electromagnetic forces between two materials in close proximity cause elongation of bonds as the materials slide past each other. When the attractive force is broken, the elastic energy stored in the elongated bond is converted to kinetic energy (the surface atom snaps loose and vibrates, e.g.). A portion of that kinetic energy converts to heat through dissipative mechanisms common to all acoustic processes in solids. It is this dissipation that is the non-conservative part of friction.

 

[rcgldr]

update - I mis-read some website articles, updating my post. Some article mention degrees of freedom for a system, but a change in state, even if total energy is conserved, does not mean it's a conservative force. I added another post below.

[STRIKE]The concept of a non-conservative force only holds true if some form of energy, like heat, is ignored. Since heat energy is just a form of kinetic energy of the molecules, by including heat energy as part of the system, then friction is a conservative force. [/STRIKE]

In the case of friction, one possible explanation is a type of hysteresis near the boundary between the two sliding surfaces, due to non-elastic collisions between the components of the surfaces. The results would be a conversion of mechanical energy into heat energy at near the surface boundary.

 

[Andrew Mason]

The concept of a non-conservative force only holds true if some form of energy, like heat, is ignored. Since heat energy is just a form of kinetic energy of the molecules, by including heat energy as part of the system, then friction is a conservative force.

Friction is non-conservative because heat is produced, not because heat is ignored.

Heat is not "just a form of kinetic energy of the molecules". It is a special form of kinetic energy in which the added molecular kinetic energy follows a Maxwell-Boltzmann distribution.

If friction caused all of the molecules to move in the same way, it could be a conservative force: one could potentially recover all of the energy from those moving molecules in the form of useful work. But friction does not do that. That energy cannot be recovered as useful work. That is why friction is non-conservative.

AM

 

[Andy Resnick]

Electromagnetic forces between two materials in close proximity cause elongation of bonds as the materials slide past each other. When the attractive force is broken, the elastic energy stored in the elongated bond is converted to kinetic energy (the surface atom snaps loose and vibrates, e.g.). A portion of that kinetic energy converts to heat through dissipative mechanisms common to all acoustic processes in solids. It is this dissipation that is the non-conservative part of friction.

This model, or something close to it, does partially account for observed stick-sip behavior:

http://prb.aps.org/abstract/PRB/v81/i24/e245415

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TH9-442B7XB-HX&_user=10&_coverDate=08%2F31%2F1979&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1529165193&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=fb0d3c5f05c4fd0bf9818b034cbbec5a&searchtype=a

http://pre.aps.org/abstract/PRE/v58/i2/p2161_1

It's interesting- both experiments involve motion within the bulk, not at interfaces. IIRC, there was some report using AFM or laser tweezers to resolve individual events, but I can't seem to locate it... something like this:

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVX-3V6XKDR-G&_user=10&_coverDate=11%2F20%2F1998&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1529168053&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3d382ec1c575d374ff12b6f4949cac00&searchtype=a

or this:

http://onlinelibrary.wiley.com/doi/10.1002/jemt.20382/pdf

 

[marcusl]

The concept of a non-conservative force only holds true if some form of energy, like heat, is ignored. Since heat energy is just a form of kinetic energy of the molecules, by including heat energy as part of the system, then friction is a conservative force.

This is incorrect. A conservative force does no work when a particle(s) is (are) moved in a path that ends where it starts. If you slide an object over another and then slide it back to the starting position, work is definitely done, and appears as heat. Friction is non-conservative.

 

[rcgldr]

A conservative force does no work when a particle(s) is (are) moved in a path that ends where it starts.

Corrected my previous post. I was tired when I posted that, and had recalled some article about non-conservative forces and degrees of freedom which I can't find any more, other than the the wiki article. The wiki article mentions degrees of freedom, although it's not clear to me what the exact point is.

Nonconservative forces arise due to neglected degrees of freedom.

http://en.wikipedia.org/wiki/Conservative_force#Nonconservative_forces

 

[K^2]

It's not just a closed path that does no work. It's closed path in phase-space. That is, you need to have coordinates for position and coordinates for velocity/momentum of each particle. Any closed path in that space does no work under conservative forces.

 

[marcusl]

It's not just a closed path that does no work. It's closed path in phase-space. That is, you need to have coordinates for position and coordinates for velocity/momentum of each particle. Any closed path in that space does no work under conservative forces.

In fact, the path doesn't have to be closed. If the work done in passing from point A to point B is independent of path, the force is conservative. I quoted just the simplest and most intuitive case.