“Hooke’s law”的概念、定义、翻译、参考文献-科学参考

Hooke’s law

Physics

The stress applied to any solid is proportional to the strain it produces within the elastic limit for that solid. The ratio of longitudinal stress to strain is equal to the Young modulus of elasticity (see elastic modulus). The law was first stated by Robert Hooke in the form ‘Ut tensio, sic vis.’

Mathematics

The law that says that the tension in a spring or a stretched elastic string is proportional to the extension. Suppose that a spring or elastic string has natural length l and actual length x. Then the tension T = (λ‎/l)(x−l), where λ‎ is the modulus of elasticity, or T = k(x−l), where k is the stiffness.

Consider the vertical motion of a particle (mass m) suspended from a fixed support by a spring (stiffness k, natural length l). Let x be the length of the spring at time t. By using Hooke’s law, the equation of motion $m \ddot{x} = m g - k (x - l)$ is obtained. The equilibrium position is given by 0 = mg−k(x−l); that is, x = l + mg/k. Letting x = l + mg/k + X gives $\ddot{X} + ω^{2} X = 0$ , where ω‎² = k/m. Thus the particle performs simple harmonic motion about the equilibrium.
http://webphysics.davidson.edu/applets/animator4/demo_hook.html An interactive illustration of Hooke’s law.

Geology and Earth Sciences

The law, named after Robert Hooke, which describes the behaviour of perfectly elastic materials in terms of a straight-line relationship between stress and strain in such materials. Strain is directly proportional to the applied stress provided the medium remains elastic (i.e. the elastic limit is not exceeded); stress is equal to the strain multiplied by a constant of elasticity (Young’s modulus). The law also states that stress divided by strain is a constant. See also elastic constants.

单词	Hooke’s law
释义	Hooke’s law Physics The stress applied to any solid is proportional to the strain it produces within the elastic limit for that solid. The ratio of longitudinal stress to strain is equal to the Young modulus of elasticity (see elastic modulus). The law was first stated by Robert Hooke in the form ‘Ut tensio, sic vis.’ Mathematics The law that says that the tension in a spring or a stretched elastic string is proportional to the extension. Suppose that a spring or elastic string has natural length l and actual length x. Then the tension T = (λ‎/l)(x−l), where λ‎ is the modulus of elasticity, or T = k(x−l), where k is the stiffness. Consider the vertical motion of a particle (mass m) suspended from a fixed support by a spring (stiffness k, natural length l). Let x be the length of the spring at time t. By using Hooke’s law, the equation of motion $m \ddot{x} = m g - k (x - l)$ is obtained. The equilibrium position is given by 0 = mg−k(x−l); that is, x = l + mg/k. Letting x = l + mg/k + X gives $\ddot{X} + ω^{2} X = 0$ , where ω‎² = k/m. Thus the particle performs simple harmonic motion about the equilibrium. http://webphysics.davidson.edu/applets/animator4/demo_hook.html An interactive illustration of Hooke’s law. Geology and Earth Sciences The law, named after Robert Hooke, which describes the behaviour of perfectly elastic materials in terms of a straight-line relationship between stress and strain in such materials. Strain is directly proportional to the applied stress provided the medium remains elastic (i.e. the elastic limit is not exceeded); stress is equal to the strain multiplied by a constant of elasticity (Young’s modulus). The law also states that stress divided by strain is a constant. See also elastic constants.
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