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In his answer to the question Can the coefficient of static friction be less than that of kinetic friction? Chad Orzel says:

As an aside, the static/kinetic coefficient model is actually pretty lousy. It works as a way to set up problems forcing students to deal with the vector nature of forces, and allows some simple qualitative explanations of observed phenomena, but if you have ever tried to devise a lab doing quantitative measurements of friction, it's a mess.

My question is are there better methods that don't use coefficient friction idea, and if coefficient is so lame why are all the physics book still using this idea?

Qmechanic
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jastyles
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2 Answers2

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Friction is a complicated process that involves different mechanisms. Friction at surfaces is fundamentally an adhesive process - see my answer to How is frictional force dependent on normal reaction? for more on this. However friction can also come from deformation of the material under the surface. Any process that causes mechanical energy to be converted to heat will manifest as a frictional force.

Give this complexity it is surprising that something as simple as Amonton's law works at all, but in many cases it is a good approximation and we teach it to students because it is both useful and simple to understand. In this respect Chad Orzel's comments are excessively critical.

However once you start to do detailed measurements of friction you find the friction coefficients are not constants but depend on the sliding velocity and the normal load as well as other factors specific to the sliding surfaces. For example from personal experience I found that if you contact very clean glass surfaces they will stick to each other so strongly that you get microscopic fractures as they slide. In this case the force is due to mechanical energy being converted to heat by a fracturing process.

So my view would be that the traditional friction coefficient approach taught to students is a good starting point. Once you look more closely you quickly see the limitations of friction coefficients, but the trouble is that once you look closely the systems and energy dissipation mechanisms become very complex and different from system to system.

John Rennie
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When I used to teach physics labs, I introduced frictional forces by attaching a force sensor to a block and then slowly and steadily applying more force until the block started to move, at which point I pulled it with constant speed. If I did my job properly, the result was a curve on the screen which looked like the following cartoon:

Force vs. time for an object under the influence of friction

After doing this a few times with different objects, we would conclude that there are two regimes at play here. When the object isn't moving, friction would match whatever force I applied, up until a limit. Once that limit was reached, friction would exert a constant force. In that sense, there are two parameters - the maximum static friction force, and the value of the sliding friction force.

This would kick off the lab which was designed to test what factors influenced those two parameters. For a given pair of surfaces, students would observe that those two parameters are both roughly proportional to the normal force between the surfaces, with the conclusion being that

$$F_{s,max} = \mu_s F_N \qquad F_{k} = \mu_k F_N$$

where $mu_s$ and $\mu_k$ were coefficients which depended on the nature of the two surfaces in contact.


The fact that this "law" could be arrived at by undergraduates during a 3 hour lab should be an indication that it may be a dramatic oversimplification. That being said, it is a remarkably good approximation to reality, as long as you are willing to allow $\mu_s$ and $\mu_k$ to be empirical parameters which may change moment to moment. And really, as long as nothing dramatic is happening to the surfaces or in the environment, their values are surprisingly consistent trial to trial.

If we need to, we can always develop more sophisticated models - see e.g. this chapter of an online robotics textbook. To do this, we might apply our coarse approximation to a specific scenario and stress-test it to find its limitations and shortcomings, and then modify the model to make it more applicable. For example, in the cartoon above, we might enhance our model to quantiatively predict the shape of the transition between the static and sliding regimes.

Do these laws break down at some point? Yes. Are there surfaces and materials which are poorly described by these laws? Yes, certainly. But I love this model because it can easily demonstrate the heart of physics and empirical science in general. We observe a phenomenon, we develop a model for that phenomenon, we test the model, and we iterate until we can predict the outcomes of future experiments to our satisfaction. It doesn't matter if it's frictional forces or quantum field theory - when it comes down to it, this is what physics is.

Albatross
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