Table of Contents
What Is Hooke's Law?
Hooke's law states that the force needed to extend or compress a spring is directly proportional to the displacement from its natural length. Formulated by Robert Hooke in 1676, it is the foundation of elasticity theory. The law applies not just to springs but to any elastic material within its elastic limit — beams, rubber bands, and even molecular bonds.
The spring constant k (stiffness) measures how much force is needed per unit displacement. A higher k means a stiffer spring. Hooke's law is linear, meaning doubling the displacement doubles the force. This linearity breaks down beyond the elastic limit, where permanent deformation occurs.
Hooke's Law Formula
Spring Constants
| Application | k (N/m) |
|---|---|
| Soft pen spring | 10-50 |
| Screen door spring | 100-500 |
| Car suspension spring | 20,000-50,000 |
| Railroad car spring | 500,000+ |
Frequently Asked Questions
What is the elastic limit?
The elastic limit is the maximum stress a material can endure and still return to its original shape when the load is removed. Beyond this limit, permanent (plastic) deformation occurs and Hooke's law no longer applies. For springs, exceeding the elastic limit means the spring won't return to its original length.
How does spring constant relate to natural frequency?
The natural frequency of a spring-mass system is f = (1/2pi) × sqrt(k/m). A stiffer spring (higher k) gives higher frequency, while more mass (higher m) gives lower frequency. This relationship governs everything from clock pendulums to earthquake building response to musical instrument design.