On extracting momentum from supports: the bullet in the beam problem

TL;DR

This paper investigates how momentum is transferred from supports to a beam when a bullet strikes it, revealing insights relevant to phenomena like the chain fountain.

Contribution

It introduces a simple model demonstrating how the support environment influences momentum transfer in beam dynamics.

Findings

Upward velocity of the beam varies with bullet entry point.

Momentum transfer depends on support interactions.

Illustrates mechanism behind chain fountain dynamics.

Abstract

To gain insights into momentum transfer from the supporting environment, we consider the simple problem of a bullet, fired from below, into a wooden beam resting on two supports. The resulting upward velocity of the beam strongly depends on where the bullet enters the beam; this dependence is due to upward momentum extracted by the beam from its supports. Our simple example illustrates the momentum transfer mechanism exploited in the remarkable dynamics of the chain fountain.