Elastic Potential Energy

When a railroad car runs into a spring bumber at the end of the track, the spring is compressed as the car is brought to a stop. If there is no friction, the bumper springs back, and the car rolls away in the opposite direction. During the interaction with the spring, the car's kinetic energy has been " stored " in the elastic deformation of the spring.

The work must do on the spring to stretch it from an elongation x1 to a greater elongation x2 is

1/2kx2^2-1/2kx1^2.


Now we need to find the work done by the spring on the body in a displacement from x1 to x2 the spring does an amount of work Wel given by




Wel =1/2kx1^2 -1/2kx2^2.


and elastic potential energy as
U = 1/2kx^2

Wel=U1-U2=-delta U.