Falling chains as variable mass systems: theoretical model and experimental analysis

TL;DR

This paper presents a theoretical and experimental study of falling chains, showing that a variable mass system model explains the acceleration of a folded U-chain, aligning well with experimental data, unlike the pile-chain.

Contribution

It introduces a variable mass system model for falling chains, highlighting the role of tension forces and energy conservation, with experimental validation.

Findings

Folded U-chain falls faster than gravity due to tension forces.

Model matches experimental data across different chain types.

Pile-chain behavior differs, not explained by the same model.

Abstract

In the present paper we revisit, theoretical and experimentally, the fall of a folded U-chain and of a pile-chain. The model calculation implies the division of the whole system into two subsystems of variable mass, allowing to explore the role of tensional contact forces at the boundary of the subsystems. This justifies, for instance, that the folded U-chain falls faster than the acceleration due to the gravitational force. This result, which matches quite well with the experimental data independently of the type of chain, implies that the falling chain is well described by energy conservation. We verify that these conclusions are not observed for the pile-chain motion.