Hooke's law
Force scales linearly with displacement for elastic materials.
Hooke's law is an empirical principle in physics describing the behavior of elastic materials. It states that the force required to stretch or compress a spring is directly proportional to the distance of that deformation, provided the deformation is small relative to the spring's total possible change in length. This relationship is expressed as \( F = kx \), where \( k \) is a constant representing the spring's stiffness, and \( x \) is the displacement from its relaxed position. The law is named after the 17th-century British physicist Robert Hooke, who first announced it in 1676 as a Latin anagram, later publishing the solution in 1678 as *"ut tensio, sic vis"*—meaning "as the extension, so the force." Hooke claimed he had known the law since 1660. The principle is fundamental to devices such as the spring scale, manometer, galvanometer, and the balance wheel of mechanical clocks. In the balance wheel, the torque from the coiled spring is proportional to the wheel's angular displacement, giving oscillations a nearly constant period. Similarly, Bourdon tubes rely on Hooke's law, where gas pressure inside a coiled metal tube creates a force that unwinds it proportionally to the pressure. The law is a first-order linear approximation; it fails when forces exceed certain limits, as no material can be compressed or stretched indefinitely without permanent deformation. Many materials deviate from Hooke's law well before reaching those elastic limits. In modern elasticity theory, Hooke's law generalizes to state that strain is proportional to stress, but the proportionality factor becomes a tensor for complex stresses and strains. For a homogeneous rod with uniform cross-section, this yields a stiffness directly proportional to its area and inversely proportional to its length. The law also applies to torsional springs, where torque is proportional to angular displacement, and to shearing or bending deformations in objects like rubber blocks or steel beams.
- field
- Physics
- nationality
- British
- known_for
- Hooke's law (ut tensio, sic vis)
Lore & Background
Hooke’s law is the empirical principle that the force needed to extend or compress a spring is linearly proportional to the distance of that deformation, provided the displacement is small relative to the spring’s total possible deformation. The constant of proportionality, known as the spring’s stiffness, is characteristic of the particular spring. The law was first stated in 1676 by the British physicist Robert Hooke as a Latin anagram, the solution of which he published in 1678: “as the extension, so the force.” Hooke claimed he had been aware of the law since 1660. The relationship holds for many elastic bodies and materials, which are termed linear-elastic or Hookean. However, it is only a first-order linear approximation; it fails when forces exceed a certain limit, as no material can be compressed beyond a minimum size or stretched beyond a maximum size without permanent deformation or a change of state. Many materials deviate from Hooke’s law well before those elastic limits are reached. The law is the fundamental principle behind the spring scale, the manometer, the galvanometer, and the balance wheel of the mechanical clock. In the balance wheel, the torque from the coiled spring is proportional to the angle turned, giving oscillations of a nearly constant period. Bourdon tubes also rely on the law, where gas pressure inside a coiled metal tube creates a force that unwinds it by an amount proportional to the pressure.
Reader's Guide
Hooke's law is a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It holds for many situations where an elastic body is deformed, but fails once forces exceed certain limits, as no material can be compressed beyond a minimum size or stretched beyond a maximum size without permanent deformation. The modern theory of elasticity generalizes Hooke's law to say that strain is proportional to stress, with the proportionality factor becoming a tensor for complex objects. This generalization allows deduction of the relation between strain and stress for complex objects in terms of intrinsic material properties, such as a homogeneous rod with uniform cross section behaving like a simple spring with stiffness directly proportional to its cross-section area and inversely proportional to its length.
Did You Know?
- The law applies to torsional springs, with torque proportional to angular displacement.
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