Hooke's Law ｜ Mechanical Properties of Solids ｜ Don't Memorise

What are Elastic and Plastic deformations? Well, deformation means the change in shape and or size of the body. And the force which deforms an object is called deforming force. Elastic deformation is the case of deformation where the body regains its original shape as soon as the deforming force is removed. But what really happens? In a state of deformation, there is a restoring force generated inside the body resisting the deformation. Yes, a restoring force! When the body is in equilibrium, this restoring force is equal in magnitude to the deforming force and acts in opposite direction. And as soon as we remove the deforming force, this restoring force comes into play and restores Plastic deformations on the other hand are the deformations that permanently change the shape of the body. The applied force here is simply too much for the body to bear and that results in permanent deformation. Now which objects show elastic deformation and which ones show plastic deformations? Generally all the objects show both type of deformations. Yes for instance, if we just keep extending the spring forever, there will be a certain limit beyond which the length won't increase further. And if we try to apply more force, the spring may loosen and end up breaking. So the spring shows elastic deformation up to some extent, beyond which it results in plastic deformation. Spring is like a common example. Generally almost every object shows both elastic as well as plastic nature. The elastic limits depends on the deforming force applied on the object and the properties of the material they are made up of. And it is important for engineers to know the elastic limits of things such as metal beams and concrete. That is, the limit to which they can uphold the load without getting permanently deformed or cracked. Now we come to an extremely important topic. The Hooke's Law. Robert Hooke, an English physicist, stated that the empirical law in 1660, which is today known by the name Hooke's law. What does empirical mean? It means the law was derived using observations. It states, for elastic deformation in a string, the deforming force is directly proportional to change in length. Consider a spring of length L, whose one end is fixed from the end. Suppose the stretching force F is applied on the other end. Now let the change in its length be delta L. The law states that the force F is directly proportional to delta L. Now what do we mean in mathematics when one quantity is directly proportional to the other? It means that one thing is some constant times the other. So we can write force F is K times delta L, where K is the proportionality constant. This is the mathematical form of Hooke's law. In some textbooks, you must have noticed the presence of negative sign on the right side of this equation. The negative sign comes due to the slightly different version of the Hooke's law being followed. We can also define Hooke's law as, the restoring force is directly proportional to change in length and this of course is valid for elastic deformation only. The force taken here is the restoring force and not deforming force. The negative sign only tells us that the restoring force is opposite to the direction in which the length is changing. Another thing is that this law is not only valid for elastic deformation in a spring, it is also valid for elastic deformation in any material. But there is an assumption that this law is valid when the forces and deformations are relatively small. Also there is a modified version of Hooke's law. It says that in an elastic deformation, the stress experienced by a body is directly proportional to strain. Before understanding this modified version, we need to understand what stress and strain mean. And we will do that in the next video.