# Potential energy stored in a spring...

by Kevin Jones
Tags: energy, potential, spring, stored
 P: 1 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.
Emeritus
PF Gold
P: 9,772
 Quote by Kevin Jones 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.
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;
 Quote by Kevin Jones answer would be helpful in Watts or Horse power
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.

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