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In this work we propose an extension to the analytical one-dimensional modelproposed by E. Gnecco (Phys. Rev. Lett. 84:1172) to describe friction. Ourmodel includes normal forces and the dependence with the angular direction ofmovement in which the object is dragged over a surface. The presence of thenormal force in the model allow us to define judiciously the frictioncoefficient, instead of introducing it as an {\sl a posteriori} concept. Wecompare the analytical results with molecular dynamics simulations. Thesimulated model corresponds to a tip sliding over a surface. The tip issimulated as a single particle interacting with a surface through aLennard-Jones $(6-12)$ potential. The surface is considered as consisting of aregular BCC(001) arrangement of particles interacting with each other through aLennard-Jones $(6-12)$ potential. We investigate the system under severalconditions of velocity, temperature and normal forces. Our analytical resultsare in very good agreement with those obtained by the simulations and withexperimental results from E. Riedo (Phys. Rev. Lett. 91:084502) and Eui-SungYoon (Wear 259:1424-1431) as well.

Velocity, temperature and normal force dependence on friction: An analytical and molecular dynamic study