Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

HOOKE’S LAW OF ELASTICITY

England, 1660. The size of a material deformation is directly proportional to the deforming force.

CROSS REFERENCE: NEWTON’S LAW OF UNIVERSAL GRAVITATION AND BOYLE’S GAS LAW.

During the year that Hooke discovered his law, Dutch peas-
ants (Boers) settled in South Africa, and water closets arrived
in England from France. The Irish natural philosopher Robert
Boyle described his research showing that the removal of air
from a chamber extinguishes a flame and kills small animals,
which suggested that combustion and respiration may be related
processes.

Hooke’s Law of Elasticity states that if an object, such as a metal rod or spring, is elongated by some distance, x, the restoring force F exerted by the object is proportional to x:

Here, k is a constant of proportionality that is often referred to as the spring constant when Hooke’s Law is applied to springs. Hooke’s Law is an approximation that applies for certain materials, such as steel, which are called Hookean materials because they obey Hooke’s Law under a significant range of conditions. For other materials, such as aluminum, Hooke’s Law has a more restricted use that applies only to a portion of the elastic range of the material. Rubber objects are non-Hookean because of their very complex responses to applied forces. For example, the stiffness of rubber is very sensitive to temperature and the rate at which a force is applied.

Students most often encounter Hooke’s Law in their study of springs where the law relates the force F, exerted by the spring, to the distance x that the spring is stretched. The spring constant k is measured in force per length. The negative sign in F = –kx indicates that the force exerted by the spring opposes the direction of displacement. For example, if we were to pull the end of a spring to the right, the spring exerts a “restoring” force to the left. The displacement of the spring refers to its displacement from equilibrium position at x = 0.

The spring constant provides an indication of the stiffness of the spring. A large value for k indicates that the spring is stiff, whereas a low value for k means that the spring is loose. As another example, consider a mass hanging from a spring. The initial position of the end of the spring is

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