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Hooke's correspondence with Newton during 1679–1680 not only mentioned this inverse square supposition for the decline of attraction with increasing distance, but also, in Hooke's opening letter to Newton, of 24 November 1679, an approach of "compounding the celestial motions of the planets of a direct motion by the tangent & an attractive ...
Later, in 1686, when Newton's Principia had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the Principia, and said Newton owed the idea of an inverse-square law of attraction to him – although at the same time, Hooke disclaimed any credit for the curves and trajectories ...
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 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.
Hooke remained bitter about Newton claiming the invention of this principle, even though Newton's 1686 Principia acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system, [6] as well as giving some credit to Bullialdus. [7]
Newton would need an accurate measure of this constant to prove his inverse-square law. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him, ultimately a frivolous accusation. [8]: 204
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is Δ E p = 1 2 k ( r 2 − r 1 ) 2 {\displaystyle \Delta E_{p}={\frac {1}{2}}k(r_{2}-r_{1})^{2}} where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units. [3] The newton is named after Isaac Newton. As with every SI unit named for a person, its symbol starts with an upper case letter (N), but when written in full, it follows the rules for capitalisation of a common ...