Friction laws

In textbooks you can find two friction laws: The law of viscous friction and Coulomb's law.

Viscous friction

This law simply says that the friction force F_F is proportional to the relative sliding velocity v between a solid and a liquid or between two liquid layers:

The proportionality factor (the greek letter gamma) is often called damping constant. The effect of viscous friction is that the oscillation amplitude of the harmonic oscillator decays exponentially.

This kind of friction can be proven mathematically. That is, it can be derived from Statistical Mechanics and Fluid Mechanics. It also holds in cases of thick fluid lubricants between two solids.

This is an empirical law for the friction force between two sliding solids. It was published by Charles Augustin de Coulomb (1736-1806) more than 200 years ago:

1. The friction force is independent of the apparent contact area between the sliding surfaces.
2. The friction force is proportional to the load N, i.e., the force perpendicular to the sliding surface which presses the two solids together. The proportionality factor is called friction coefficient.
3. The kinetic friction F_K (i.e., the force to keep a body sliding at a constant velocity) does not depend on the sliding velocity. It is less than or equal to the static friction F_S, i.e., the force to start sliding.

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Coulomb actually summarized what was already known at his time: Leonardo da Vinci discovered the first part. The second part goes back to the french engineer Amonton in 1699. Coulomb contributed the third part. He also measured the friction coefficients of many materials.

In the experiment the load is determined by the weight of the slider. That is, N = g M where g is the acceleration of gravity. Its value is 9.81 m/sec².