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Author Topic: Hozirontal spring and vertical spring  (Read 13940 times)
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Fu-Kwun Hwang
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on: October 25, 2009, 03:53:44 pm » posted from:Taipei,T\'ai-pei,Taiwan

, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit.
\vec{F}=-k \vec{d}
where
   \vec{d}, d=x-x_0 is the displacement of the end of the spring (x) from its equilibrium position (x_0);
   vec{F} is the restoring force exerted by the material; and
   k is the force constant (or spring constant).
The potential energy of a spring can be expressed as U(d)=\int -(-kx)dx|^d=\tfrac{1}{2}kdx^2

It becomes more complicated when a spring is hang in a vertical direction under gravity g.
If the end of the spring is y_0 when there is no mass attached to the spring.
The equilibrium position becomes y_0-\frac{m*g}{k} when a mass m is attached.
The motion is still a Simple Harmonic motion (SHM) if the mass is pushed/pulled away from the equilibrium position and released. What will be the spring force and potential energy look like as a function of y?

I hope the following simulation will help you find out the answer.

There are two tabbed panel in the simulation. One for horizontal spring and another one for vertical spring under gravity.
You can drag it to move the mass away from the equilibrium position, it will show external force and spring force.

The blue vurve is the force as a function of d : F_x(x-x_0) or F_y(y-y_0)
The red curve is the kinetic energy K=\tfrac{1}{2}mv^2
The green curve is the spring energy: U_k=\tfrac{1}{2}kd^2, where d=x-x_0 or d=y-y_0

The black vurve is the potential energy U_{mg}=m g d
The yellow curve is the sum of U_k+U_{mg}

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* springxy.gif (18.07 KB, 524x580 - viewed 674 times.)
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Fu-Kwun Hwang
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Reply #1 on: April 05, 2010, 11:17:30 pm » posted from:Taipei,T'ai-pei,Taiwan

Click eye(image) to view the same simulation with different view (modified by Ahmed

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Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
  • Please feel free to post your ideas about how to use the simulation for better teaching and learning.
  • Post questions to be asked to help students to think, to explore.
  • Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!


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