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Potential energy stored in a spring... 
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#1
Jul1506, 10:25 AM

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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
Jul1506, 03:19 PM

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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; [tex]F = kx[/tex] 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; [tex]E_{p} = \int^{x}_{0} F \; dx = \int^{x}_{0} kx \; dx[/tex] [tex]E_{p} = \frac{1}{2}kx^{2}[/tex] Where k is the spring constant, which can be approximated using the following formula; [tex]\sqrt{\frac{{\color{red}K}}{\rho}} = a\sqrt{\frac{{\color{red}k}}{m}}[/tex] 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, [itex]\rho[/itex] 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; 


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