Elasticity is the property of an object or material due to which it restores its original shape after distortion. The more precisely an object restores to its original configuration the more elastic it is. When a spring is stretched, it exerts a restoring force which tends to bring it back to its original length. This restoring force is generally proportional to the amount of stretch.
The English scientist Robert Hooke discovered a law in 1660, according to which the extension of a spring is directly proportional to the load (deforming force) applied to it. Under these conditions the object returns to its original shape and size upon removal of the load. It is known as Hook’s Law.
Mathematically, Hooke’s law states that the applied force F (N or kg·m/s2) equals a constant k (N/m or kg/s2) times the displacement or change in length x (meters), or F = kx. Sometimes Hooke’s law is formulated as F = −kx. In this expression F no longer means the applied force but rather means the equal and oppositely directed restoring force that causes elastic materials to return to their original dimensions.
Many materials obey this law as long as the load does not exceed the material’s elastic limit. When plotted on a graph, the line shows a direct variation. Stress is the force on unit areas within a material that develops as a result of the externally applied force. Strain is the relative deformation produced by stress. Hooke’s law may also be expressed in terms of stress and strain. Hooke’s law in simple terms says that strain is directly proportional to stress.
Objects that quickly regain their original shape after being deformed by a force, often obey Hooke’s law. Hooke’s law only holds for some materials under certain loading conditions. Steel obeys Hooke’s law throughout its elastic range. For aluminium, Hooke’s law is only valid for a portion of the elastic range. Rubber is generally regarded as a “non-hookean” material because its elasticity is stress dependent and sensitive to temperature and loading rate. Spring operated weighing machines, stress analysis and modelling of materials use Hooke’s law.
Image sources: https://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html
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