Resolving Tensions Surrounding Massive Pulleys

TL;DR

This paper clarifies the tension distribution in systems with massive pulleys, addressing common ambiguities and proposing experimental methods to measure tension profiles, thus enhancing understanding in introductory mechanics.

Contribution

It introduces two novel approaches to resolve tension distribution ambiguities involving elastic deformation of pulleys or strings, with practical experimental proposals.

Findings

Two compact resolutions for tension distribution ambiguities

Experimental methods to measure tension profiles

Enhanced understanding of pulley-string interactions

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.