Is There a Conservation Equation for Spring Forces and Potential Energy?

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Homework Help Overview

The discussion revolves around the conservation equations related to spring forces and potential energy, particularly in the context of a mass attached to a spring. Participants explore the nature of spring forces as conservative forces and the implications for energy conservation in different scenarios.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants question whether there is a conservation equation specifically for springs and discuss the relationship between potential energy and the conservation of energy principle. They consider scenarios involving horizontal and vertical spring setups and the role of gravitational potential energy.

Discussion Status

The discussion is active, with participants providing insights into the conservation of energy equation as it applies to springs. There is acknowledgment of different conditions affecting the equations, such as the presence of gravitational potential energy in vertical setups. Some participants express agreement on the formulations discussed.

Contextual Notes

Participants are navigating the complexities of energy conservation in different spring configurations, including horizontal and vertical orientations. There is a focus on ensuring all relevant energy terms are included in the equations being considered.

pb23me
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Homework Statement


I just have a question about the force of a spring. Since the force of a spring force is a conservative force, is there a conservation equation for springs? Also, when a mass is put on a spring and it streches out fully, at this point velocity is zero and potential energy is at its max. What can i set potential energy equal to at this point?


Homework Equations





The Attempt at a Solution

 
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pb23me said:

Homework Statement


I just have a question about the force of a spring. Since the force of a spring force is a conservative force, is there a conservation equation for springs?
yes, it is similar to the conservation of energy equation with the added terms of the spring's potential energy
Also, when a mass is put on a spring and its streches out fully, at this point velocity is zero and potential energy is at its max. What can i set potential energy equal to at this point?
Use the conservation of energy equation! What is the potential energy of a spring?
 
ok so would it be kxi2+mvi2=kxf2+mvf2
 
pb23me said:
ok so would it be kxi2+mvi2=kxf2+mvf2
Yes, if the the spring was horizontal and no other forces (like friction) acting..If the spirng was hanging vertical and the mass released, you'd have to include the gravitational potential energy change also. (It's a good idea to not drop the '1/2' term, even though it cancels out in this first example).
 
ok so if it were hanging vertically it would be mgyi+1/2mvi2+1/2kxi2=mgyf+1/2mvf2+1/2kxf2?
 
pb23me said:
ok so if it were hanging vertically it would be mgyi+1/2mvi2+1/2kxi2=mgyf+1/2mvf2+1/2kxf2?
yes, indeed.:approve:
 
:smile:awsome maybe you could take a look at my other prob entitled simple harmonic motion haha
 

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