Hourglass of constant weight as an illustrative example of a system with a variable mass

TL;DR

This paper revisits the classic hourglass of constant weight problem, offering a corrected derivation and emphasizing the pedagogical value of momentum flux in understanding systems with variable mass.

Contribution

It provides a corrected derivation of the problem and highlights the educational importance of momentum flux in variable mass systems.

Findings

Corrected the derivation of equation (8) from the original article.

Emphasized the pedagogical usefulness of momentum flux.

Clarified the physical understanding of systems with variable mass.

Abstract

We provide an alternative approach to a problem posed in the article "Hourglass of Constant Weight" by Volker Becker and Thorsten P\"{o}schel, which appeared in Granular Matter 10 (2008), 231-232, i.e. 14 years ago. Our goal to return to this article after so much time is purely pedagogical. Although there is a slight and subtle inaccuracy in the derivation of equation (8) in the work of Becker and P\"{o}schel, which we correct, we use this circumstance only to give a detailed pedagogical exposition of an excellent physical problem and to show the pedagogical usefulness of the concept of momentum flux when considering the mechanics of systems with variable mass.