Hooke’s Law and Spring Constant

Hooke’s Law and Spring Constant

Hooke’s law which we sometimes refer to as the law of elasticity was discovered by an English scientist Robert Hooke in the year 1660. For comparatively small distortions of an object, the displacement or size of the distortions is directly proportional to the distortion force or load, says the Hooke’s Law. However, the spring constant relates to Hooke’s law.

Due to this reason, the object gets back to its original size when the load on the object is removed. In other words, it can be explained owing to the fact that minute displacement of their ions, atoms and molecules from their normal positions is also directly proportional to the force which causes the displacement to take place.

spring constant

Meaning of Hooke’s Law

The force which deforms an object can be applied to a solid object by subjecting the solid to stretching, compression, squeezing, twisting or bending. An application of Hooke’s Law can be easily seen in a metal wire which exhibits the behaviour of elasticity, as when it is stretched by an applied force, the small increase in its length doubles every single time when the force which is applied on the metal wire is doubled.

 Equation of Hooke’s Law

In mathematical terms, We can state Hooke’s Law through the following equation:


As per this equation, F is the force which we apply and it equals a constant. K represents a constant that is k times the displacement or change in the length of an object which we represent by x.


F = Applied force
k = Constant for displacement
x = Length of the object
The value of k is dependent on the kind of elastic material, its dimensions and its shape.

When we apply a relatively large value of force, the elastic material’s deformation is many times larger than the amount which we expect as per the Hooke’s Law.

Although, the material still remains elastic as before and returns back to its original size and when we removes the force that we apply it retains its shape. At times, Hooke’s Law can be:

F = -kx

Here, F represents the equal and oppositely applied to restore causing the elastic materials to get back to their original dimensions.

Spring Constant

We can easily understand Hooke’s Law in connection with spring constant. Moreover, this law states that the force which we require for compression or extension of a spring is directly proportional to the distance to which we compress or stretch it.

In mathematical terms, we can state this as follows:

F ∝ x

Here, F represents the force that we apply on the spring. And x represents the compression or extension of the spring which we usually express in metres.

spring constant

Let us understand this more clearly with the following example:

It stretches a spring by 50 cm when it has a load of 10 Kg. Find its spring constant.

Here, it has the following information:

  • Mass (m) = 10 Kg
  • Displacement (x) = 50cm = 0.5m

Now, we know that,

Force= mass x acceleration

=> 10 x 0.5= 5 N.

As per the Spring Constant formula

k = F/x

=> -5/0.5= -10 N/m.

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