Spring Potential Energy: Difference between revisions

Revision as of 22:52, 4 December 2015

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

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Connectedness

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Spring Potential Energy: Difference between revisions

Revision as of 22:52, 4 December 2015

Contents

The Main Idea

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See also

Further reading

External links

References

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@@ Line 9: / Line 9: @@
 The formula for Ideal Spring Energy is
-U<sub>s</sub>=
+'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''
-<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>
 where:
-k<sub>s</sub>= spring constant[[File:]]
+'''k<sub>s</sub>'''= spring constant
-s<sup>2</sup>= stretch measured from the equilibrium point;
+'''s<sup>2</sup>'''= stretch measured from the equilibrium point;
 ===A Computational Model===
+An oscillating spring can be modeled by the following:
-How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
+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==