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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.
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.
A coil spring with a variable rate, usually achieved by having unequal distance between turns so that as the spring is compressed one or more coils rests against its neighbour. Rubber band A tension spring where energy is stored by stretching the material. Spring washer Used to apply a constant tensile force along the axis of a fastener ...
Under this model, if the material is put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress.
The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar. In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread.
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.