Is Hooke’s Law Applicable to All Elastic Materials?

Spring is a deformable item that may be distorted by force and then return to its original shape once the force has been removed. The strain experienced by most materials when a small amount of tension is applied by the tightness of the chemical bonds inside the substance. The chemical structure of the material and the nature of chemical bonds present are closely related to its stiffness.

Hooke’s law states that the displacement or amplitude of deformation is proportional to the deforming force or load for relatively mild deformations of an item. The law was given by the English scientist Robert Hooke in 1660. In these IIT-JEE notes, we will understand the meaning and concept of Hooke’s Law and find out whether Hooke’s Law applies to all elastic materials. 

Hooke’s Law

According to Hooke’s Law:

F = -kx,

Where 

F is the spring force

k is the spring constant

x is compression of the spring

The negative sign represents that the restoring force is in the opposite direction of the spring force. 

Where k is a constant factor characteristic of the spring (i.e., its stiffness) and x is minimal when seen from the prospect of the entire possible deformation of the spring. When the load is removed or replaced, things transform into their original shape and dimensions. The elastic behaviour of Hooke’s law can be explained by the displacement of constituent molecules, atoms, or ions from normal locations.     

Hooke’s equation holds true when an elastic body is distorted, like guitarists playing a guitar string and wind blowing on a tall building. A linear-elastic or Hookean body or substance is one for which this equation can be assumed. Hooke’s law is the first example of a traditional explanation of elasticity, which is the quality of an item or material that allows it to return to its original shape after being distorted. The ability to return to its original shape after being distorted is known as a “restoring force.” This restoring force is often proportional to the amount of “stretch” experienced, according to Hooke’s Law.

While answering questions, we must keep in mind that Hooke’s law can be used to approximate the genuine effects of applied forces on springs and other elastic bodies, which is a first-order linear approximation. However, since there is a specific limit to squeezing or stretching of materials, irreversible deformation or change of state, it will eventually fail if the forces exceed this limit. Before the elastic limits are reached, some materials diverge noticeably from Hooke’s rule.

Is Hooke’s Law Applicable to All Elastic Materials?

Hooke’s law does not apply to all elastic materials. Hooke’s law is an accurate approximation for most solid bodies, as long as the forces and deformations are minimal enough. As a result, Hooke’s law is widely applied in all research and engineering fields. Seismology, acoustics and molecular mechanics are based on this law. And spring scale, balance wheel, and manometer also use this law.

Hooke’s law is generalised in the contemporary theory of elasticity, which states that the strain (deformation) of an elastic item or substance is proportional to its stress. However, because these stresses may have several individual parts, the “proportionality factor” can be a linear map that can be defined by a combination of real numbers rather than a single real number.

In its common form, this law allows you to determine the relationship between strain and stress for complicated objects based on the intrinsic qualities of the materials they’re composed of. When a homogeneous rod with a uniform cross-section is stretched, it behaves like a simple spring, with a stiffness k that is exactly proportional to its cross-section area and inversely proportional to its length.

Hooke’s law can be studied through graphs of Hooke’s law. This graph is the deformation between ∆L versus applied force F. 

Application of Hooke’s Law 

This law is employed in all disciplines of science and engineering. There is no substitute for Hooke’s law when it comes to understanding the behaviour of elastic materials.     

Things like a manometer, the clock’s balance wheel, a guitar and a spring scale use this principle. Many devices like seismology, acoustics and molecular mechanics are built on this law. 

Conclusion

Hooke’s law describes the elastic characteristics of materials only in the region where force and displacement are proportionate. Hooke’s law can alternatively be stated as a stress-strain relationship.

Minor displacements of their constituent molecules, atoms, or ions from normal locations are proportional to the force that generates the displacement. Although, for most solid bodies, If the forces and deformations are minimal, Hooke’s law can be used to approximate the elasticity. However, to answer whether Hooke’s law applies to all elastic materials, it does not apply to all.