The Brachistochrone: An excellent problem for all levels of physics students

TL;DR

This paper discusses the brachistochrone problem as an educational tool across different student levels, emphasizing qualitative understanding over quantitative solutions in introductory physics courses.

Contribution

It introduces an activity for qualitative exploration of the brachistochrone problem suitable for various student levels and evaluates student performance.

Findings

Freshmen, juniors, and graduate students can engage with the problem qualitatively.

Qualitative discussions enhance understanding of physics concepts.

The activity is accessible and adaptable for different educational levels.

Abstract

The classic brachistrochrone problem is standard material in intermediate mechanics. Many variations exist including some accessible to introductory students. While a quantitative solution isn't feasible in introductory classes, qualitative discussions can be very beneficial since kinematics, Newton's Laws, energy conservation and motion along curved trajectories all play a role. In this work, we describe an activity focusing on a qualitative understanding of the brachistochrone and examine the performance of freshmen, juniors and graduate students. The activity can be downloaded at https://w3.physics.arizona.edu/undergrad/teaching-resources .