Tomlinson Movie
Macroscopic Friction
The law of Leonardo (da Vinci)
The law of Euler and Amontons
The law of Coulomb
Historical abstract
Adhesion models
Friction Force Microscopy
Principle of measuring
Measuring Topology
Measuring Friction
Both Channels
Self assessment
Tomlinson's mechanism
Phenomenology I
Phenomenology II
Mechanical adiabaticity
Distinguish positions
Playing Tomlinson
Friction - a pinning problem
2D Friction
Critical Curves
Historical Background
Research Projects
Simulator Applet
The first Picture
The Panels
Post processing

Leonhard Euler (1707-1783)


Euler on the 10 franc banknote (Serie 1975 - 1995)

The scientist Leonhard Euler, who was born in Basel and later moved to St.~Petersburg is famous for his work in the field of mathematics. Less is known about his important contributions in the field of friction physics. He studied theoretically the mechanism of the sliding motion of a block on an inclined plane. He adopted the model of rigid interlocking asperities as the cause of frictional resistance. (Euler considered Leonardo's experiments of the sliding block on the inclined plane.}

He assumed that the friction force results from gravitational forces, trying to minimize the potential energy of the block. He found the relation between inclination angle a and friction coefficient m. We find this relation also by equating the friciton force with the accelerating force:

Assuming a velocity-independent friction coefficient, he found, that for the critical angle a the acceleration of the block should be exceedingly small, since gravity is nearly compensated by kinetic friction. This result was against the experimental facts, where sliding started relatively fast. He concluded, that one has to distinguish between static and kinetic friction and that static friction is always larger than kinetic friction. With these assumptions he was able to describe the motion of a block on an inclined plane. Euler was the first who distinguished between static and kinetic friction.

  Guillaume Amontons (1663-1705)                  Charles Augustin Coulomb (1736-1806)

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