Elastic Potential Energy

Elastic potential energy

In physics, potential energy is the energy held by an object because of its "position" of a physical quantity. For example, the higher an object is, the more gravitational potential energy it has. Elastic potential energy is stored when an elastic object is stretched, compressed, or bent. This energy is the result of the object's ability to return to its original shape after the applied force is removed. Beyond the elastic limit, a material no longer stores the elastic potential energy.

Elastic potential energy and kinetic energy

When an arrow is shot from a bow, the elastic energy stored in the string, the limb, and even the arrow itself, is transferred into the kinetic energy of the arrow.

When a ball is returned with a racket, the kinetic energy of the ball and the racket is stored as the elastic energy of the strings and even the ball itself for a moment, and is then transferred back into the kinetic energy of the ball.

Elastic potential energy of a linear spring

A linear/Hookean spring follows Hooke's law:

$$F_s=k\Delta x$$

where $F_s$ is the spring force, $\Delta x$ is the changed length of the spring, $k$ is a constant with a unit of $N/m=kg/s^2$. Specifically, $\Delta x=x-x_0$, where $x$ is the current length of the spring, and $x_0$ is the original/natural length of the spring.

The elastic potential energy of a linear spring is

$$U_s=\frac{1}{2}k(\Delta x)^2$$

which shows the elastic potential energy is stored proportional to the square of the changed length of the spring.