Elastic potential energy is an important concept in physics in which the energy has been stored in elastic materials as they are stretched or compressed. It forms the central explanation of the working of any system, from simple springs to the more complex types of machinery.

Definition: Energy Elastic potential energy, E p, is the energy of an elastic object when it is deformed. This can be in a stretching motion as with springs or in a compressing motion as with rubber bands. As soon as the deforming force is removed, the stored elastic potential energy will cause the object to resume its original shape.

Formula 

As per Hooke's law, the stretch force applied to the spring is directly proportional to the amount of stretch.

In other words,

The force needed to stretch the spring is proportional to its displacement. It is described as 

F =kx

Where,

• k = spring constant 

• x = displacement

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

Where,

• P.E = elastic potential energy and it's measured in Joule.

Solved Problems

Problem 1: A compressed spring has the potential energy of 20 J and its spring constant is 200 N/m. Calculate the displacement of the spring.

Solution:

Given,

Potential energy P.E = 40 J,

Spring Constant k = 200 N/m,

The Potential energy formula is given by

the displacement is given by

x = √2P.E / k

  = √2×40 / 200

  = 0.632 m

 

Problem 2: The vertical spring is attached to a mass of 5 kg which has been compressed by 10m. Determine the force constant of the spring.

Solution:

Given: Mass m = 5kg

Distance x = 10 m

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

k = F / x

  = 49 / 10

  = 4.9 N/m

 

Other Related Sections

NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for kids| Learning Concepts I Practice Worksheets I Formulas | Blogs | Parent Resource