Analyzing collisions in classical mechanics using mass-momentum diagrams

TL;DR

This paper demonstrates how mass-momentum diagrams can simplify the analysis of one-dimensional collisions in classical mechanics, eliminating calculations and providing visual insights for undergraduate students.

Contribution

It introduces the use of mass-momentum diagrams as a calculation-free tool for analyzing collisions, including in the center-of-mass frame.

Findings

Mass-momentum diagrams visually represent collision quantities.

The diagrams allow analysis without calculations.

They are useful for understanding collisions in different reference frames.

Abstract

We show the value of mass-momentum diagrams for analyzing collision problems in classical mechanics in one dimension. Collisions are characterized by the coefficient of restitution and the momentum of the interacting particles both before and after the collision. All those quantities are presented in the mass-momentum diagrams without the need to do any calculations. We also show that the same diagrams can be used to investigate collisions with respect to the center-of-mass system. In this case, also, we do not need to do any calculations to obtain the momentum. Since we give an alternative way of looking at collisions in classical mechanics, this article is aimed at undergraduate-level students.