Analytic expression for pull-or-jerk experiment

TL;DR

This paper provides an analytical solution to the pull-or-jerk experiment, identifying the critical pulling speed and illustrating the interplay between speed and elasticity through a phase diagram.

Contribution

It introduces a novel analytic model for the experiment, determining the critical conditions for which string breaks first under pulling.

Findings

Derived an explicit equation of motion for the system.

Identified the critical pulling speed for string breakage.

Presented a phase diagram showing the effects of elasticity and speed.

Abstract

This work focuses on a theoretical analysis of a well-known inertia demonstration, which uses a weight suspended by a string with an extra string that hangs below the weight. The point in question is which string, the upper or lower, will break when pulling down on the bottom edge of the lower string at a constant pulling speed. An analytic solution for the equation of motion allows us to identify the critical value of the pulling speed, beyond which the string breaking varies from one to the other. The analysis also provides us a phase diagram that illustrates the interplay between the pulling speed and the string's elasticity in the pull-or-jerk experiment.