Hooke's law

In physics, Hooke's law of elasticity states that if a force (F) is applied to an elastic spring or prismatic rod (with length L and cross section A), its extension is linearly proportional to its tensile stress σ and modulus of elasticity (E):

Related Topics:
Physics - Elasticity - Force - Extension - Proportional - Tensile stress - Modulus of elasticity

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:sigma = E cdot arepsilon

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or

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:Delta L = rac{1}{E} imes F imes rac{L}{A} = rac{1}{E} imes L imes sigma

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It is named after the 17th century physicist Robert Hooke, who initially published it as the anagram ceiiinosssttuv, which he later revealed to mean ut tensio sic vis, or as the extension, the force.

Related Topics:
17^th century - Robert Hooke - Anagram

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This "law" is actually an approximation that holds for only some materials under certain loading conditions. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "hookean" materials. Steel is a good example of a linear-elastic material, and Hooke's law is valid for it throughout its elastic range (i.e. for stresses below the yield strength). For some other materials, such as Aluminum, Hooke's law is only valid for a portion of the elastic range. For these materials a proportional limit stress is defined, below which the errors associated with the linear approximation are negligible.

Related Topics:
Steel - Yield strength - Aluminum

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Materials such as rubber, for which Hooke's law is never valid, are known as "non-hookean". The stiffness of rubber is not only stress dependent, but is also very sensitive to temperature and loading rate.

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The graph below shows a stress versus strain curve for a typical linear-elastic material.

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Applications of the law include spring operated weighing machines. Originally the law applied only to stretched springs, but subject to physical constraints it also applies to compression springs.

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