Resolving Tensions Surrounding Massive Pulleys

Abstract

The distribution of string tension on the contact line between an ideal string and a massive pulley is a frequently-discussed but incompletely-posed problem that confronts students in introductory mechanics. We highlight ambiguities in the usual presentation of this problem by the massive Atwood's machine and discuss two compact resolutions that treat situations where the pulley or the string elastically deform. We propose experiments that can be developed in an intermediate laboratory to determine the tension profile.