All About Elastic Potential Energy

The energy accumulated as a result of applying force to deform an elastic item is known as elastic potential energy. The energy is stored until the force is removed, at which time the item returns to its original shape and resumes its function.  This is the amount of energy stored in an object due to its deformation. You may find elastic potential energy in any item that can be distorted and returned to its original shape. Rubber bands, sponges, and bungee cords are just a few examples of objects that this may apply to.

When you distort these items, they automatically return to their original shape. An item that is not influenced by elastic potential energy, such as a sheet of aluminium foil, serves as a counter-example. When you compress a sheet of paper into a ball, it will not return to its original shape when you let go. Due to the deformation, the item may be squeezed, stretched, or twisted.

Elastic Material

• The coil spring of a wind-up clock
• An archer’s bow that is stretched out
• A twisted diving board just before a diver leaps
• A twisted rubber band that propels a toy aeroplane
• A bouncing ball has been crushed as it bounces against a brick wall

Although the elastic limit of an object designed to contain elastic potential energy is usually rather high, all elastic things have a load limit. An item will not return to its original shape if it is deformed beyond its limit of elasticity.

In past generations, wind-up mechanical watches powered by coil springs were common. We no longer use wind-up smartphones because no materials have a high enough elastic limit to store elastic energy with a high enough energy density.

The elasticity of a material determines its capacity to transmit energy in this form. The amount of energy stored in the spring is determined by:

• The length of time the spring has been deformed (stretched or compressed).
• The level of force required to break or compress a spring by one metre is this constant.

The Formula For Computing Elastic Potential Energy In An Ideal Spring

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

F =kx

k = spring constant

x = displacement

The elastic potential energy formula of the spring stretched is given as,

P.E.= 1/2Kx²

The spring force is conservative, meaning it has potential energy because k is a positive number. According to the concept of work, the area beneath a force vs. displacement curve represents the work done by the force. 

Genuinely Elastic Materials

Some elastic materials, such as rubber bands and flexible plastics, can operate as springs, but they commonly exhibit hysteresis, which means that when the material is compressed, the force vs. extension curve travels a different route than when it relaxes back to its equilibrium condition.

Luckily, the same fundamental method of applying the definition of work that we used to create a perfect spring also works for elastic materials. Regardless of the form of the curve, we may always use the area under the force vs. extension curve to calculate the elastic potential energy.

Hooke’s Law can be expressed mathematically in the following ways.

f = – kx

f = kx

The formula is sometimes written with a negative sign to indicate that Hooke’s Law is a force applied, although the negative version is also acceptable. Here, x denotes the spring’s displacement, while k is the spring constant.

This constant measures a spring’s stiffness that is specific to each spring. The spring constant is affected by various parameters, including the material of the spring and the diameter of the wire wrapped, among many others.

Equation

The equation for elastic potential energy is:

Elastic potential energy = force x distance of displacement.

• Elastic potential energy (Joules, J)
• (Newtons per metre, N/m) spring constant
• The distance between the current (equilibrium) location and the old (equilibrium) position (metres, m)

Its form and substance determine the elastic qualities of spring. As a result, the spring constant varies depending on the item.

Conclusion

Elastic potential energy is essential in many mechanical systems, such as shock absorbers in vehicles, since spring can stay in compression or stretched position for long periods without losing energy.

Shock absorbers in automobiles are designed to decrease the effect on passengers by absorbing forces generated by driving on rough roads. Regenerative braking systems, which utilise stored energy to provide the vehicle with a slight power boost, are another application of elastic potential energy in cars.