The "coin-through-the-rubber" trick: an elastically stabilized invagination

TL;DR

This paper analyzes the elastic deformation involved in the magician's coin-through-rubber trick, modeling the invagination formation and stability using Hookean and neo-Hookean elasticity theories.

Contribution

It introduces an analytical model for the rubber invagination in the trick and compares it with numerical solutions, enhancing understanding of the elastic stability involved.

Findings

Hookean model predicts invagination formation

Neo-Hookean model confirms stability analysis

Analytical and numerical results agree on stability conditions

Abstract

A spectacular trick of close-up magicians involves the apparent passing of a coin through a rubber sheet. The magic is based on the unusual elastic response of a thin rubber sheet: the formation of an invagination, stabilized by friction and elasticity, which holds the coin. By pressing on the coin, the invagination becomes unstable, and the coin is released. We describe the deformation analytically using a simple Hookean description, and examine the stability of the invagination. We finally compare the prediction of the Hookean analysis with numerical solutions of the neo-Hookean model, and provide a brief commentary on the origins of the trick.