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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.
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.
For example, if a person places a force of 10 N at the terminal end of a wrench that is 0.5 m long (or a force of 10 N acting 0.5 m from the twist point of a wrench of any length), the torque will be 5 N⋅m – assuming that the person moves the wrench by applying force in the plane of movement and perpendicular to the wrench.
These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these. This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
is the torque exerted by the spring in newton-meters, and is the angle of twist from its equilibrium position in radians κ {\displaystyle \kappa \,} is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient , torsion elastic modulus , rate , or just spring constant , equal to the change in torque ...
For ring closing reactions, it is an example of enantioselectivity, wherein a single enantiomer of a cyclization product is formed from the selective ring closure of the starting material. In a typical electrocyclic ring closing, selection for either conrotatory or disrotatory reactions modes still produces two enantiomers.
An example of this is a common elastic band, composed of long chain (rubber) polymers. By stretching the elastic band you are doing work on the system and the band behaves like a conventional spring, except that unlike the case with a metal spring, all of the work done appears immediately as thermal energy, much as in the thermodynamically ...