Experimental study of viscous friction in undergraduate physics laboratory: introduction of phase diagrams to analyse dynamic equilibrium

Abstract

In this work we propose using phase diagrams to explain the dynamical behaviour of simple mechanical systems. First the motion of the system x t ( ) is experimentally measured, and then the derivatives, v t ( ) and a t ( ), are obtained from it and the motion equation = f x v a ( , , ) 0 is represented graphically. This idea is applied to the study of a system with linear viscous drag, explaining the evolution of the system towards the dynamical equilibrium point corresponding to the limit velocity. The phase diagrams of the viscous drag are compared with those of the Coulomb drag, which is not continuous and does not necessarily lead to a uniformly accelerated motion. The method is illustrated by an experiment in a dynamic track with magnetic damping. The use of phase diagrams allows for the checking the linearity of this damping. Moreover it allows for the identification of the existence of a small Coulomb drag between the track and the cart that appears as a small discontinuity of the function a v ( ) when the direction of the movement changes.