# Potential energy stored in a spring

1. Jul 15, 2006

### Kevin Jones

potential energy stored in a spring....

Help needed :)

I guess this will be easy for some of you put there...but not me it seems. What I need to know is how to calculate the potential energy that can be stored in a compression spring. I currently have a project of mine that is a design for pedal assistance on a bicycle so the answer would be helpfull in Watts or Horse power.
If somebody could help me and tell me the calculation I would very much appreciate it.

Kevin.

Ps, any ideas on the subject of potential energy and its application for pedal assistance is also welcome.

2. Jul 15, 2006

### Hootenanny

Staff Emeritus
Hi there Kevin and welcome to PF,

Are you familiar with Hooke's law? Hooke's law states that the force exerted by a Hookean material is equal to the product of the spring constant and the strain (distance compressed) and can be expressed thus;

$$F = -kx$$

Now, any work done on the spring (by an applied stress) will be stored as potential energy. Work done is defined as the integral of force with respect to displacement, therefore;

$$E_{p} = \int^{x}_{0} F \; dx = \int^{x}_{0} kx \; dx$$

$$E_{p} = \frac{1}{2}kx^{2}$$

Where k is the spring constant, which can be approximated using the following formula;

$$\sqrt{\frac{{\color{red}K}}{\rho}} = a\sqrt{\frac{{\color{red}k}}{m}}$$

Note the different cases of K and k. The uppercase 'K' is the bulk modulus of the material, the lower case k is the spring constant, $\rho$ represents the density, m is the mass of an atom and a represents the atomic spacing (the space between the atoms).

You say in your original post;
These are units of power not energy; to express work done in terms of power a time reference is required (power is work done per unit time). I hope this is helpful for you and I look forward to assisting you in your project.

Last edited: Jul 15, 2006