Studying springs in series using a single spring

TL;DR

This paper presents an innovative experiment using a single spring with marked segments to study the static properties of springs in series, verifying Hooke's law and the relationship between segment and whole spring constants.

Contribution

It introduces a simple, effective method to analyze series spring systems with one spring, enhancing educational demonstrations and understanding of spring mechanics.

Findings

Hooke's law holds for the combined spring system

The spring constant of segments relates predictably to the whole spring

The method provides accurate results with minimal setup

Abstract

Springs are used for a wide range of applications in physics and engineering. Possibly, one of its most common uses is to study the nature of restoring forces in oscillatory systems. While experiments that verify the Hooke's law using springs are abundant in the physics literature, those that explore the combination of several springs together are very rare. In this paper, an experiment designed to study the static properties of a combination of springs in series using only one single spring is presented. Paint marks placed on the coils of the spring allowed us to divide it into segments, and considered it as a collection of springs connected in series. The validity of Hooke's law for the system and the relationship between the spring constant of the segments with the spring constant of the entire spring is verified experimentally. The easy setup, accurate results, and educational benefits make this experiment attractive and useful for high school and first-year college students.