# Fermilab

## Inquiring Minds

Why does friction increase with roughness to a point and then start to decrease with increasing roughness?

Please can you help me to explain an experiment result. My sister who is currently studying her A-level had just done her coursework on friction. Where different rough surfaces variable by the different degree on sand paper in it's energy needed to move a fixed mass upon it. They find from their result that as predicted the friction increases as the 'roughness' increases yet only to a certain point. After that to everyone's surprise it decreases.

So far the only theory that seems to agree with anything is perhaps the amount of negative repulsion is only to a fix amount and that the degree of compression also. Hence there is a maximum amount of friction that is available. Yet I can not explain the reason for the decline. One rather strange idea that had come from a biological friend suggested that it may had been due to the rounded shape of the atom and that it acts as ball bearing^Å his theory seems slight impossible to me, yet it's the best we had come up so far.

Another idea, is one that I got from another experiment of perhaps the negative charges got to a very high degree that the repulsion acts to push away the mass? Like when we have air blowing over a track?

Sorry about my primitive physic knowledge as I had only study it to GCSE.

Thank you for your time and help.

Janet Kan

London UK

Hi Janet Kan,

I am willing to bet your sister was using the f=(coeff. of friction)xN to describe friction in her experiment. Where N is the normal force it is equal to the weight or load of the object if it is sliding on a level surface. This is the classical description of friction. As you know friction acts in the opposite direction to the motion and is measured parallel to the surfaces that are touching. Classical friction can be summed up in the following four conjectures:

1. Friction is proportional to the load or the normal force

2. Depends on the nature of the surfaces

3. Does not depend on the apparent area of contact of the surfaces

4. Friction is independent of velocity

Friction is much more complicated than the classical description suggests. Scientists have been trying to figure what actually causes friction for centuries. In fact the first experiments on the subject were conducted by di Vinci. In your sisters experiment she found that as she increased the roughness the friction increased to a point then friction started to decrease with increasing roughness. It has been experimentally shown that the friction may decrease with roughness and in the other extreme very smooth surfaces may have enourmous frictional forces, this is what happens in cold welding. This seems contrary to the classical explaination because it has been shown experimentally that friction depends on the contact area of the two objects. Where contact area is the area that actually touches the other object. It is not the apprarent area of contact. It it is the area of all the microscopic contact points between the two objects. The more contact area the higher the friction. This explains your sisters results. As the sandpaper got to a certain roughness the grains of sand where larger which decreased the over all contact area and reduced the friction. The grains are larger so there will be fewer contact points. One example of this is when you wear cleats on a smooth hard surface you slip all over the place. Where as if you wore the same cleats on a soft surface the cleats would sink in and have a higher coeff of friction because the amount of area actually in contact with the ground is much higher.

The model of molecular cohension tried to explain this effect by describing friction as the cohesion of molecules between surfaces. The molecules of one substance would have to come close enough to the molecules of the other substance to interact. These contact points should produce some type of wear. This model was proven wrong when Jacob Israelachvili found clear evidence for a wear-free friction in the 1970's.

The current model used to explain wear-free friction is based on the vibrations of atomic lattices. The basic concept is friction occurs when atoms close to one surface are set in motion by the sliding action of atoms in the opposing surface. These vibrations are called phonons which are really sound waves which eventually get converted into heat. The amount of mechanical energy(the energy needed to keep the object moving) converted to phonons depends on the nature of the sliding substance because different solids vibrate a certain specific frequencies. If one solid has many of the same frequecies as another then friction will be high.

An excellent discussion of this can be found in Scientific American pg. 74 "Friction at the Atomic Scale" by Jacqualine Krim, Oct 96. Another older but still informative article can be found in Scientific American pg. 55, "Friction" by Frederic Palmer, Feb 1951.

One last thing it has been shown that classical conjectures 1 & 3 can be replaced with "Friction is proportional actual contact area between the two objects". Normally, this does not effect simple physics experiments because as the load increases the surfaces flattens out and the contact area increases proportionally. Additionally, conjecture 4 is only approximately true for medium velocity experiments. Which for your sisters experiment was an ok assumption. Actually, friction does depend on velocity. If you stop your car you have to ease up on the brakes as you slow down because friction increases as you slow down. This effect has been observed for objects travelling at bullet velocities. Friction decrease as speed increases.