Energy dissipation and trapping of particles moving on a rough surface

Abstract

We report on an experimental, numerical, and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $\ensuremath{\theta}$, the inclination angle of the rough surface, and ${E}_{\mathrm{ki}},$ the initial kinetic energy. When the angle of inclination is larger than some critical value, $\ensuremath{\theta}>{\ensuremath{\theta}}_{T},$ the ball moves at a constant average velocity, which is independent of the initial conditions. For an angle $\ensuremath{\theta}<{\ensuremath{\theta}}_{T},$ the balls are trapped after moving a certain distance. The dependence of the traveled distances on ${E}_{\mathrm{ki}},$ $D,$ and \ensuremath{\theta} is analyzed. The existence of two kinds of mechanisms of dissipation is thus brought to light. We find that for high initial velocities the friction force is constant. As the velocity decreases below a certain threshold the friction becomes viscous.