Hyperbolic cosine function in physics. (24th November 2020)

• Record Type: Journal Article
• Authors: Bonnet, Isabelle; Gabelli, Julien
• Is Part Of: European journal of physics. Volume 42:Number 1(2021)
• Publication Date: 2020-11-24
• Subjects: catenary -- chainette -- physics -- hyperbolic cosine; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/1361-6404/ab9c8f
• Languages: English
• ISSNs: 0143-0807

Abstract

Abstract: A catenary is the shape that an electric cable takes under its own weight if suspended only at its ends between two pylons. A rope hung between two masts is also described with a catenary equation which is based on the hyperbolic cosine function. We propose here to approach the hyperbolic cosine function with two simple experiments using a beaded chain. We first study the static form of a chain whose ends are suspended between two poles, when the distance between the two poles varies. Then, we study the dynamics of the same chain falling from the edge of a table. The simplicity of these two experiments, which can be done at home, makes them appropriate for undergraduate students interested in practicals.