Potential energy stored in a spring

[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.

 

[Hootenanny]

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;

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.

 

[kyle8921]

Dear Kevin,

It's great to hear about your project on pedal assistance for a bicycle. Potential energy stored in a spring is an important concept in physics and engineering, and it is essential for understanding the mechanics of your project.

To calculate the potential energy stored in a compression spring, you will need to know two values: the spring constant (k) and the displacement of the spring (x). The spring constant is a measure of how stiff the spring is, and it is usually given in units of Newtons per meter (N/m). The displacement is the distance that the spring is compressed from its equilibrium position, and it is also measured in meters (m).

The formula for calculating potential energy stored in a spring is:

Potential energy (U) = 1/2 * k * x^2

So, to calculate the potential energy stored in your compression spring, you will need to measure the spring constant and the displacement of the spring. Once you have those values, you can plug them into the formula to find the potential energy in Joules (J). To convert this to Watts or horsepower, you will need to know the time it takes for the spring to compress and release, as power is measured in units of energy per unit time.

As for potential energy and its application for pedal assistance, you can think of the spring as a way to store energy. When the rider pedals, they are exerting a force on the spring, compressing it and storing potential energy. This potential energy can then be released to assist the rider in pedaling, making it easier for them to move the bicycle forward. This is a basic concept of how potential energy can be used for pedal assistance, and there are many other factors and designs that can be incorporated for a more efficient and effective system.

I hope this helps and best of luck with your project!

Sincerely,