# Elastic Potential Energy Formula

## Elastic potential energy formula

Elastic potential energy is the potential energy stored by stretching or compressing an elastic object by an external force such as the stretching of a spring. It is equal to the work done to stretch the spring which depends on the spring constant k and the distance stretched.

According to Hooke’s law, the force applied to stretch the spring is directly proportional to the amount of stretch.

In other words,

Force required to stretch the spring is directly proportional to its displacement. It is given as

$F\,&space;=\,&space;-\,&space;kx$

Wherein,

k = spring constant

x = displacement

The Elastic Potential Energy Formula of the spring stretched is given as

$P.E\,&space;=\,&space;\frac{1}{2}kx^{2}$

Where,

P.E = elastic potential energy and it’s expressed in Joule.

Example 1

A compressed spring has potential energy of 40 J and its spring constant is 200 N/m, calculate the displacement of the spring.

Solution:

Given:

Potential energy P.E = 20 J,

Spring Constant k = 200 N/m,

The Potential energy formula is given by

P.E = 1 / 2 kx2

the displacement is given by

x = √2P.E / k

= √2×40 / 200

= 0.632 m

Example 2

The vertical spring is linked to a load of mass 5 kg which is compressed by 10m. Determine the Force constant of the spring.

Solution:

Given: Mass m = 5kg

Distance x = 10 cm

Force formula is given by

F = ma

= 5 kg × 9.8 m/s2

= 49 N

Force in the stretched spring is

F = k x

Force Constant k is given by

= F / x

= 49 / 10

= 4.9 N/m