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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
This relationship is known as Hooke's law. A geometry-dependent version of the idea [a] was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", [5] [6] a linear relationship commonly referred to as Hooke's law.
Hooke's law may be written in terms of tensor components using index notation as = +, where δ ij is the Kronecker delta. The two parameters together constitute a parameterization of the elastic moduli for homogeneous isotropic media, popular in mathematical literature, and are thus related to the other elastic moduli ; for instance, the bulk ...
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
The top part is a plot of the linear relation between force F and elongation X according to Hooke's law (solid line). The red half correspond to positive elongation and pulling force, the blue part to negative elongaton (compression) and pushing force. The slope of the curve is Hooke's constant "k".
The most general linear relation between two second-rank tensors , is = where are the components of a fourth-rank tensor . [1] [note 1] The elasticity tensor is defined as for the case where and are the stress and strain tensors, respectively.
427 ± 15 GPa [7] (predicted) Water: 2.2 GPa (0.32 Mpsi) (value increases at higher pressures) Methanol 823 MPa (at 20 °C and 1 Atm) Solid helium: 50 MPa (approximate) Air 142 kPa (adiabatic bulk modulus [or isentropic bulk modulus]) Air 101 kPa (isothermal bulk modulus) Spacetime: 4.5 × 10 31 Pa (for typical gravitational wave frequencies of ...
However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Mathematically, F = − k x , {\displaystyle \mathbf {F} =-k\mathbf {x} ,} where F is the restoring elastic force exerted by the spring (in SI units: N ), k is the spring constant ( N ·m −1 ), and x is the ...