Sliding down a rough curved hill

Abstract

Abstract In this paper, we analyse the process of a particle sliding down an arbitrary curved hill in the presence of friction. We show that in this case, the kinetic friction force turns out to be effectively dependent on the speed. We find that the final speed for each concave (convex) profile should be less (greater) than that for the corresponding inclined plane. In the limit of extremely small final speed or profiles of the hill close to linear, the final speed does not depend on the shape of the trajectory even in the presence of kinetic friction. As an illustrative example, we perform the calculation of the final speed for a concave hill in the form of a quarter circle. We also derive the shape of the curved hill profile for which a body can slide down at a constant speed.