Energy Dissipation and Trapping of Particles Moving on a Rough Surface

TL;DR

This study investigates how particles move on rough surfaces, revealing critical angles for motion and trapping, and identifying two dissipation mechanisms: constant friction at high velocities and viscous friction at low velocities.

Contribution

It provides a combined experimental, numerical, and theoretical analysis of particle motion, highlighting the transition between different dissipation regimes and the conditions for trapping.

Findings

Particles move at constant velocity above a critical angle.

Trapping occurs below the critical angle depending on initial energy.

Two dissipation mechanisms: constant friction and viscous friction.

Abstract

We report 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, $\theta$, the inclination angle of the rough surface and $E_{ki}$, the initial kinetic energy. When the angle of inclination is larger than some critical value, $\theta>\theta_{T}$, the ball moves at a constant average velocity which is independent of the initial conditions. For an angle $\theta < \theta_{T}$, the balls are trapped after moving a certain distance. The dependence of the travelled distances on $E_{ki}$, $D$ and $\theta$. is analysed. 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.