Known more specifically as Hooke’s law of elasticity, it effectively states that the extension or contraction of a spring is directly proportional to the force applied to it. Or, in other terms - the strain is proportional to the stress.
Mathematically, Hooke’s law states that
- x is the displacment of the spring’s end from equilibrium (SI; measured in meters).
- F is the restoring force exerted by the spring on that end (SI; measured in Newtons).
- k is a constant known as the spring constant, basically a measure of the spring’s stiffness (SI; measured in N/m).
There is a negative sign on the right side of the equation because the restoring force always acts in the opposite direction of the displacement when acting linearly. For example, if I pull a spring to the right with force F, the resulting force will attempt to return the spring to the left - the opposite direction.
Hooke’s law is named after the 17th century British physicist Robert Hooke, who first proposed the law in 1660. He published the law as a Latin anagram; he published the solution in 1678 as Ut tensio, sic vis, which translates to, “As the extension, so the force.”