Classical Mechanics After Newton

Nine years after the death of Newton, Charles-Augustin de Coulomb (1736-1806) was bom in France. He has contributed a lot to electricity and magnetism. Coulomb was a military engineer who turned to physics later on. In mechaitics, he is known for his following laws on ftiction  

The maximum force of friction is independent of the magnitude of area in contact between the surfaces. 

The maximum force of friction is less and practically constant at low velocities of sliding than that at the state of impending motion. 

In the paper submitted to French Academy of Science in 1784, Coulomb showed the results of torsion test of iron wire. 

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As soon as we start this journey into the atom, we encounter an extraordinary feature of our world. When scientists began to understand the composition of atoms in the early twentieth century (Section B), they expected to be able to use classical mechanics, the laws of motion proposed by Newton in the seventeenth century, to describe their structure. After all, classical mechanics had been tremendously successful for describing the motion of visible objects such as balls and planets. However, it soon became clear that classical mechanics fails when applied to electrons in atoms. New laws, which came to be known as quantum mechanics, had to be developed. 

If we consider a classical-mechanical particle, its wave function will be large only in a very small region corresponding to its position, and we may then drop the averages in (7.114) to obtain Newton s second law. Hius classical mechanics is a special case of quantum mechanics. Equation (7.114) is known as Ehrenfest s theorem, after the physicist who derived it in 1927. 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

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