Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Details Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

1995-12-05

arxiv.org/abs/cond-mat/9512030v1

Physics

Condensed Matter

19 pages, latex, 11 postscript figures in separate uuencoded file

Scientific paper

10.1103/PhysRevE.53.6496

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.

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