Robert Hooke, an English scientist, gave the Hooke’s Law of elasticity in 1660. It states that for the relatively small deformations of an object, the size of the deformation or displacement is directly proportional to the deforming load or force. With these conditions, the object would return to its original size and shape with removal of the load.
According to the Hooke’s law, the elastic behaviour of solids can be explained by the fact that the small displacements (of molecules, atoms or ions) from their normal positions are proportional to the force which causes the displacement.
The deforming force is applied through compression, stretching, squeezing, twisting or bending a solid.
Hooke’s law states that the applied force is equal to a constant times the change in length or displacement.
Where, F is force, K is constant of proportionality and X is displacement.
STRAIN AND STRESS
Hooke’s law can also be explained in the terms of strain and stress. Strain is the deformation produced by the stress. And stress is the force on the unit areas within a material caused due to externally applied force.
Robert Hooke studied the springs and their elasticity and observed that the stress vs strain curve for a variety of materials has a linear region. Within its certain limits, the force applied or required to stretch an elastic object (eg. A metal spring) is directly proportional to that of the extension of that spring.
DIRECTION OF THE FORCE APPLIED
Even though the direction of force isn’t established, a negative sign is always added. It is because of the restoring force which causes the displacement (since the spring is already in the opposite direction). Pulling down a spring will make the spring extend downwards and the resulting force would be upwards. Thus, it is essential to make sure of the fact that the direction of the restoring force should be specified consistently while approaching elastic related mechanic problems.
USES OF HOOKE’S LAW
- Used in all branches of science and engineering
- Foundation for seismology, acoustics and molecular mechanics.
- Fundamental principle behind manometer, spring scale, balance wheel of the clock.
LIMITATIONS OF HOOKE’S LAW
- The law isn’t a universal principle and only applies to the materials as long as they aren’t stretched way past their capacity.
- It ceases to apply past the elastic limit of a material. If the material is stretched past its elastic limit, it causes permanent deformation.
- The law is only accurate for most solid bodies only and if the forces and deformations are small.