What Happens to the Excess Energy in a Compressed Spring?

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Discussion Overview

The discussion revolves around the energy dynamics involved when compressing a spring, specifically addressing the work done by an external force and the energy stored in the spring. Participants explore the relationship between applied force, work done, and energy transfer in both mechanical and electrical contexts.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether the work done by compressing a spring is equal to the energy stored, noting that the work done using a constant force seems to yield a different result than the stored energy.
  • Another participant explains that when compressing a spring with a varying force, the work done equals 1/2kx², suggesting that the additional work done with a constant force contributes to the kinetic energy of an attached mass.
  • A third participant agrees with the previous explanation, reiterating that the average force during compression leads to the conclusion that the work done is 1/2kx².
  • A later post introduces a scenario involving an electrically charged mass on a spring, proposing that when an electric field is applied, the work done results in kinetic energy and oscillation of the mass.
  • Another participant confirms the oscillation of the mass around a new equilibrium point when the electric field is applied.

Areas of Agreement / Disagreement

Participants generally agree on the concept that the work done in compressing a spring with a varying force leads to the energy stored in the spring, but there is some debate regarding the implications of using a constant force and the resulting energy dynamics in different scenarios.

Contextual Notes

The discussion includes assumptions about linear spring behavior and the effects of external forces, but does not resolve the implications of using constant versus varying forces in terms of energy transfer.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in mechanics, energy transfer, and oscillatory motion in systems involving springs and forces.

jd12345
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If you apply a force F and compress a spring of spring constant k by x distance what is the work done by us?
I know energy stored is 1/2kx2 but is the work done by us the same?
We are applying a cosntant force F and dispalcement is x so work done by us should be Fx right? And F = kx so work done by us is kx2

Where does the other 1/2kx2 go?
 
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jd12345 said:
Where does the other 1/2kx2 go?
Imagine there was a mass on the end of the spring. If you used the minimum force required to compress the spring, then that force would vary from 0 (at the start) to the maximum value of kX at full compression. The work you'd do would equal 1/2kx2. But if you use a constant force F = kX to compress the spring, then the extra work that you do goes into increasing the kinetic energy of the mass.
 
I agree with DocAl
When you start to compress(or stretch) the spring you start with zero force and increase to final force,F and F = kx. The work done = average force x extension.
If the spring behaves linearly the average force = F/2 therefore work done = kx/2 . x
= 0.5kx^2
 
Okay thank you - but one more doubt
Suppsoe a mass m attached to a spring with charge q. Suddenly electric field is switched on so it will exert a constant force right? So in this case the other 1/kx^2 goes into kinetic energy and the spring oscillates? Have i got it right?
 
That's right. The mass will oscillate about the new equilibrium point (where the net force on the mass is zero).
 

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