Symmetry in the system conformed by two blocks connected by a string with variable tension

TL;DR

This paper analyzes a two-block system connected by a string with variable tension, exploring the symmetry properties and equilibrium conditions relating angles and distances.

Contribution

It provides a systematic analysis of tension as a function of angles and distances, revealing symmetry-like properties in static equilibrium configurations.

Findings

Identifies symmetry-like relations in tension for different configurations.

Derives conditions for equal tension based on angles and distances.

Offers a comprehensive analysis of static equilibrium in the system.

Abstract

In this paper we review the system made up by two blocks connected by a string over a smooth pulley with variable tension. One block lies on an horizontal surface and the another block is hanging vertically. We carry out a complete and systematic analysis for the tension of the string as function of the angle and the horizontal distance x, at static equilibrium. We find a simmetry-like that corresponds to two different confifigurations with the same tension and obtain the relationship that must satisfy two angles or two horizontal distances to obtain equal tension.