**Elastic Potential Energy Formula **

Potential energy is the energy of an object accumulated or stored in it due to its constant position. When we consider potential energy frequently, the first thing we can conceive of is an object high-pitched in the air and falling down.

The object falling has potential energy stored in it because of its height, and when the object has a downfall, the energy will be converted into kinetic energy.

**Define Elastic Potential Energy**

Elastic potential energy is defined as the energy of an object due to existing damage to its shape. Therefore, any random object can be damaged or deformed and then can return to its initial or original shape; that object is known to have elastic potential energy. Examples of Elastic potential energy include sponges, rubber bands, bungee cords, etc.

**The Formula for Elastic Potential Energy**

We can determine the elastic potential energy by implying fundamental formula, which is cited below:

Elastic potential energy = displacement x force

It is calculated as the work done to stretch the spring, which counts on the spring constant k and the shift stretched.

The force required to straighten the spring is directly proportional to its shift or displacement.

It can be given as:

F = kx

P.E = 1 / 2 kx²

The negative sign here indicates the direction.

k = spring constant

x = displacement

**Solved Examples**

**A compressible spring has a potential energy of 20 J, and its spring invariable is 200 N/m. Determine the shift or displacement of the spring.**

Potential energy P.E = 40 J,

Spring Constant k = 200 N/m,

The Potential energy expression is yielded by

P.E = 1 / 2 kx²

And the displacement is yielded by:

x = √2P.E / k

= √2×40 / 200

= 0.632 m

**2. The vertical spring is associated with a mass load of 5 kg, which is compacted by 10m. Calculate the force constant of the spring.**

Given: mass m = 5 kg

Distance x = 10 m

The 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