Hyperbolic cosine function in physics. (24th November 2020) - Bonnet, Isabelle; Gabelli, Julien
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.