Basics of Elastic Energy

Elastic energy is the potential energy stored in an object when it is stretched, compressed or deformed.
It’s found in objects like springs, elastic bands, and rubber, which can deform elastically when subjected to a force.
By Hooke’s law, the force required to compress or extend a spring is directly proportional to the distance it is stretched or compressed.
The mathematical expression of Hooke’s Law is F = kx, where F is the force applied, x is the displacement of the spring from its equilibrium position, and k is the spring constant.

Calculating Elastic Energy

The formula used to calculate the elastic potential energy stored a spring is E = ½ k x².
In this equation, E represents the elastic potential energy, k is the spring constant, and x is the distance the spring is stretched or compressed.
Note that the formula is only valid provided that the elastic limit of the spring is not exceeded.

Elastic potential energy is a type of stored energy. It can be transferred into other forms of energy (like kinetic energy) when the stored energy is released.
An excellent illustration of this is seen in the operation of a catapult or a bow and arrow.
The concept of elastic energy is not limited to springs. It also applies to any situation where an object is deformed, such as stretching a rubber band or inflating a tyre.

In finding the elastic potential energy in problems, identify the spring constant and displacement from equilibrium position.
Take into account if an object’s elastic limit (the maximum amount it can be deformed without permanent damage) is exceeded, the object is said to be in the plastic region and will not return to its original shape when the force is removed.
Always interpret your answer in context of the problem. You must determine whether the amount of elastic potential energy found is reasonable.