What does the spring constant depend on?

Hooke’s Law is usually approached in textbooks as a black box model, in which the proportionality between the applied force on springs and their deformation is not explained grounded on parameters about the investigated system. This theoretical model, despite of its great didactic value, does not allow the construction of answers to questions such as: How do the dimensions of the spring influence its elastic constant? In this article, seeking to contribute to the construction of answers to questions like this, we present a theoretical model to represent helical springs in a linear limit. In this model, the spring constant of a spring is predicted as a function of its dimensions, its number of turns and the shear modulus of the material from which it is produced. The theoretical model built was also empirically contrasted with the use of three different springs. One of them is a low-cost plastic spring. The elastic constants of these springs and of springs built from their split were measured from data about the forces acting in these springs and their deformations. Giving empirical support to the constructed model, the results showed that the shear modulus of the springs remains constant when splitting them, and that the elastic constants are inversely proportional to the number of coils of the springs.

Keywords:
Shear; elastic constant; helical spring; Hooke’s law; shear module