Spring Potential Energy

Work in progress by scarswell3 This topic covers Gravitational Potential Energy.

The Main Idea

Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.

A Mathematical Model

The formula for Ideal Spring Energy is

U_s=¹⁄₂k_ss² where: k_s= spring constant s²= stretch measured from the equilibrium point;

A Computational Model

An oscillating spring can be modeled by the following: from __future__ import division from visual import * from visual.graph import * scene.width=600 scene.height = 760 g = 9.8 mball = .2 Lo = 0.3 ks = 12 deltat = 1e-3 t = 0 ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2)) ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow) spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01) spring.axis = ball.pos - ceiling.pos vball = vector(0.02,0,0) ball.p = mball*vball scene.autoscale = 0 scene.center = vector(0,-Lo,0) while t < 10:

   rate(1000)    
   L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()
   Fspring = -ks * L_vector
   Fgrav = vector(0,-mball * g,0)
   Fnet = Fspring + Fgrav
   ball.p = ball.p + Fnet * deltat
   ball.pos = ball.pos + (ball.p/mball) * deltat
   spring.axis = ball.pos-ceiling.pos  
   t = t + deltat
  

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

This section contains the the references you used while writing this page