# Elastic Potential Energy - Spring Potential Energy

## 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 and Elastic Potential Energy. This article exclusively deals with the concept of 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,

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

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#### Practise This Question

One end of a nylon rope of length 4.5 m and diameter 6 mm is fixed to a tree-limb. A monkey weighing 100 N jumps to catch the free end and stays there. Find the elongation of the rope and the corresponding change in the diameter. Young modulus of nylon = 4.8 x 1011 N m-2 and Poisson ratio of nylon = 0.2.