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Physics: Hooke’s Law


Mechanical physics allows investigating the nature of dynamic processes occurring routinely in solid objects. Using the principles of mechanics, it becomes possible to carry out theoretical calculations, determine the permissible rate of loading, and predict the deformation of bodies when they are subjected to physical impact. Thus, Hooke’s law is one of the fundamental rules characterizing the elastic force in bodies when they deform: for instance, springs, wires, or beams. This report provides a detailed academic study of this physical law and a discussion of its applicability.

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An Overview of Hooke’s Law

There is no doubt that any solid body has its measure of stiffness. While some objects are softer, others, on the contrary, are stronger and harder. Thus, Hooke’s mechanical law postulates that the stiffer a body is, the less it changes linear dimension when external pressure is applied to it. As a formula, this rule can be written as shown in equation [1]. The symbol k denotes the body’s numerical stiffness coefficient, while the letter x characterizes the displacement of the linear dimension when deformed. It is worth clarifying that the coefficient of elasticity k depends on both the material properties and the size of the rod. In addition, the presence of the minus sign indicates the opposite direction of the resultant elasticity force concerning the axis along which the body was compressed or uncompressed.

Based on this formula, it is possible to formulate Hooke’s law for elastic media verbally. The elastic force arising in a body when it is deformed is directly proportional to the magnitude of that deformation. It is appropriate for a more detailed understanding to consider an illustrative example explaining the possibilities of applying equation [1] to force calculations. More specifically, if weight is attached to a stretched string of length l, it is expected to stretch. The negative change in length between the two phases of the spring, multiplied by its material’s stiffness factor, will calculate the elasticity force.

There is, nevertheless, an important assumption for this law that limits its application to calculations. In particular, the elasticity force is directly proportional to length displacement only for small deformations but becomes irrelevant as the size of the object increases. Thus, the use of the formula [1] to calculate the elasticity of long bodies is not correct and leads to physical errors. Meanwhile, the use of Hooke’s law is possible only for elastic deformation models, in which the particles of the object tend to return the object to its original position after the external pressure is removed.


To summarize the above, Hooke’s law is a fundamental principle of the mechanics of elastic media, which allows us to correlate the degree of deformation of a body’s linear size with the physical force of elasticity. This report presented a mathematical formulation for this law and discussed two important aspects concerning the applicability of the principle. In particular, it was shown that Hooke’s law is relevant only for elastic and relatively small deformations.

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