Elastic potential energy refers to the energy stored resulting from a change in the shape or form of an elastic object due to a force acting on it. The stored energy is released when the force is removed. This is a form of potential energy stored between the atoms of objects. 

The energy is absorbed when stressed and released when the object is relaxed. 

An example of elastic potential energy can be observed in a slingshot. When the shape of the slingshot changes due to the force of the stone, energy is stored in it. As the slingshot is relaxed, this energy is released.    

Elastic Potential Energy:

• It refers to the energy stored due to a force applied on an elastic object, such as a spring. 
• This form of energy is dependent on the elasticity of the object being used. Elasticity refers to the ability of an object to go back to the position it was initially in before the application of a force. 
• Two factors play an essential role in the elastic potential energy of an object: the distance the object has been displaced from its original position and the amount of force applied to the object.
• Elastic objects can be stretched and deformed only up until a specific limit. Beyond this, the object will not come back to its original form. Thus, elastic potential energy can be stored within a specific limit. 
• Elastic Potential energy is different from plastic potential energy in the reversibility of the action. At the same time, elastic potential energy causes objects to come back to the original; plastic potential energy results in an irreversible change. 
• There are various applications of elastic potential energy. This concept is utilised in several mechanical devices, such as cars. 
• Vehicles have shock absorbers that work to protect passengers from high impact due to factors such as difficult roads. The shock absorbers absorb the energy from bumpy roads to protect the car and the passenger from the resulting disturbances. 
• Regenerative braking systems, too, work on the principle of elastic potential energy by using the stored energy to give vehicles a boost. 

Hooke’s Law:

• Hooke’s law was named so because it was introduced by the 17th-century physicist Robert Hooke. 
• The law states that small changes in the shape or form in the size of objects is directly proportional to the force placed on the object. 
• The formula for this law is F = kx, where F is the force on the object, k is the spring constant, and x is the displacement of the elastic object.
• The deformation of objects can be caused by stretching, squeezing, bending, or twisting. 
• The application of this law goes beyond just the stretching of a rubber band. It is used in breathing, cars, and even beds.
• Some of its shortcomings include that the law is not universal and can be applied when the deformations are small. 
• The law can only be applied to elastic objects or just the elastic areas of objects.

The Importance of Elastic Potential Energy:

• The concept of elastic potential energy is helpful in various mechanical devices as well as everyday objects,
• This form of energy is vital as it tells us how much work and power generation a particular object is capable of.
• The stored energy can be utilised in various functions and work efficiently.
• This form of energy can also be converted to kinetic energy, used in different functions and objects.
• Rubber bands, trampolines, and slingshots are some examples of elastic potential energy. 
• This energy is used in toys such as wind-up toys. Here, the toy is wound up, which requires effort as the energy is stored through the winding up. This stored energy is transformed into kinetic energy and makes the toy move. 
• Humans, too, possess elastic potential energy, as observed in walking and jumping. The Achilles tendon is responsible for storing elastic energy due to the movement and releasing it in walking. 

Conclusion:

Elastic Potential energy refers to the energy stored in objects due to their force. It is a form of potential energy that depends on the amount of force applied to the object and the distance that the object is displaced. 

The formula for elastic potential energy is ½ k.x2. 

This concept has various applications, such as rubber bands, slingshots, trampolines, diving boards, the spring of a wind-up clock, and even the human body. The elastic potential energy is stored between atoms of objects and helps them utilise this energy in movement.