Experimenting with Inexpensive Plastic Springs

Acommon undergraduate laboratory experience is the determination of the elastic constant of a spring, whether studying the elongation under a static load or studying the damped harmonic motion of the spring with a suspended mass. An alternative approach to this laboratory experience has been suggested by Menezes et al.,1 aimed at studying the dependence of the elastic constant with the length of the spring. The proposal by Menezes et al.1 consists of determining the springs elastic constant K (defined as the ratio of the elongation δ and the magnitude of applied force F) using the usual method of suspending a mass m and studying the dependence of K on the springs unstretched length L. The authors vary the length of a spring by cutting pieces off the end and obtain an experimental relation K=αL^-1⁠, with α a constant depending on the spring materials and geometrical factors. In our teaching practice we have been using the experience in Ref. 1 as an opportunity for advanced students to earn extra credit after the ordinary laboratory experience. The results we have obtained so far confirm the work of Menezes et al.1 and inevitably motivate a discussion on the dependence of the elastic constant K with some other spring parameters. The present work originates from the quest of a couple of students to determine the role of the spring coil diameter D on the value of K and α.