Elastic potential energy and spring potential energy are one of the most interesting concepts in physics. In this article, we will learn about the concepts of these topics in a detailed manner.

## What is Potential Energy?

Potential Energy is the energy possessed by a body by virtue of its position with reference to a position zero. The two common types of Potential Energy are:

- Gravitational Potential Energy
- Elastic Potential Energy

## Elastic Potential Energy

Elastic Potential Energy is the potential energy stored in an elastic material when it is stretched or compressed. The amount of energy stored is proportional to the amount stretched or compressed, as in, the more the amount of stretch, greater is the energy stored.

Have you tried jumping on a trampoline? Or ever seen someone do it? Ever noticed that the more the trampoline stretches downwards when a person jumps on it, the more they are thrown upwards? This is an example of elastic potential energy.

*Check out the picture given below.*

Among the three springs, which one do think has more potential energy? Quite clearly, the third one as it has been stretched by the greatest amount (2x), compared to the other two (0 and x). By virtue of its position, the third spring has the greatest amount of elastic potential energy in this case. You can also think of it this way. The amount of work done in stretching the spring is just being converted into energy here.

Based on Hooke’s Law, we already know that for elastic materials, the force applied by the spring is proportional to its displacement, given by the following relation.

\(F\) =\( kx\)

where,

F is applied load

x is the displacement (stretch or compression)

k is the spring constant

At the equilibrium position of such a system (where the force applied is 0), the potential energy possessed by the system is zero. To calculate the potential energy stored in the spring when it is displaced by a certain amount, the following formula can be used.

\(U\) = \(\frac{1}{2}kx^2\)

where,

U is the elastic potential energy of the system

## Spring Potential Energy

When we compress or extend a stretched spring, we experience a force equal to that applied by us in the opposite direction. But as soon as the stress is relieved, the spring attains its normal shape instantly. This is called as the spring potential energy. The elastic potential energy of the spring helps it do so. Generally, it follows Hooke’s law.

### What is Hooke’s law?

According to this Hooke’s Law, the force which is needed to change the spring’s shape is proportional to the spring’ displacement. Here, displacement is how far the spring is stretched or compressed from its original shape.

We can mathematically summarise Hook’s Law as:

**F= – k x**

Where,

‘k’ is the spring constant

‘x’ is the displacement.

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