Whip dynamics in a freely falling chain

TL;DR

This paper investigates the complex whip-like motions of a freely falling chain under gravity, revealing that the chain exhibits whip dynamics with diverging tip speeds and periodic snapping, supported by experimental evidence.

Contribution

It provides the first detailed analysis and experimental demonstration of whip-like behavior in a freely falling chain, highlighting the role of the curved region in the dynamics.

Findings

Chain exhibits whip dynamics with diverging tip speed.

The curved region of the chain is crucial for lifting and whip motion.

Experimental validation confirms the theoretical predictions.

Abstract

In this work, we examine the whip dynamics in a freely falling chain. We consider an inextensible chain with free ends in the presence of gravity hanging from a fixed pulley. If the configuration is unbalanced, the chain begins to accelerate and eventually may lift off the pulley. We show that after the liftoff, the dynamics of the chain resemble that of a whip whose tip speed diverges. The curved region of the chain plays a key role in the dynamics, lifting the chain. The chain is in free fall, yet it exhibits whip dynamics, with one end snapping upward periodically as the chain falls. We have conducted experiments demonstrating this phenomena.