Friction of a sphere rolling down a granular slope

¹ Departamento de Física de la Universidad de Santiago de Chile - Avenida Ecuador 3493, 9170124 Estación Central, Santiago, Chile
² Sorbonne Université, Université Paris Diderot and Laboratoire de Physique et de Mécanique des Milieux Hétérogenes (PMMH), CNRS, ESPCI Paris, PSL Research University - 10 rue Vauquelin, 75005 Paris, France

Received: 7 May 2018
Accepted: 7 September 2018

Abstract

The present study investigates the rolling motion of a rigid sphere moving down a granular slope. We observe that the sphere only moves steadily beyond a critical inclination that depends on the diameter and density of the sphere. The groove created on the bed surface during the passage of the sphere, grows with the diameter and density of the sphere and it is nearly independent of both the sphere speed and the slope angle. The granular resistance experienced by the rolling sphere is deduced from its dynamics. A mechanical description of the interaction between the sphere and the granular bed accounts for the experimental findings through a single adjustable parameter. A phase diagram for the sphere dynamics defined by two dimensionless parameters, namely the slope angle and the ratio of the densities of the sphere and of the grains, is proposed.