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 [[File:]]

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

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