Studying springs in series using a single spring

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.