How Do Spring Constants and Resistor Formulas Compare?

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Discussion Overview

The discussion revolves around the comparison of spring constants and resistor formulas, particularly focusing on the equations governing springs in series and parallel configurations versus those for resistors. The scope includes theoretical exploration and conceptual clarification regarding the mathematical similarities and physical differences between these systems.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes the equations for overall spring constants in series and parallel are opposite to those for resistors, prompting a question about the significance of this observation.
  • Another participant explains that while the formulas are similar due to analogous mathematical behavior, there are no physical similarities between springs and resistors.
  • A participant expresses confusion regarding the explanation, questioning why the equations for resistors in parallel do not follow the same additive principle as springs in parallel.
  • Further clarification is provided, detailing the derivation of total force for springs in parallel and total voltage for resistors in series, emphasizing that similar mathematical behavior does not imply physical similarity.
  • A later reply introduces capacitors, suggesting that similar principles apply when reversing the terms of series and parallel configurations.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the mathematical similarities between the equations, but there is disagreement regarding the implications of these similarities and the physical interpretations, leading to unresolved confusion about the concepts involved.

Contextual Notes

Participants express uncertainty about the physical interpretations of the mathematical similarities, and there are unresolved questions about the applicability of the equations across different systems (springs, resistors, capacitors).

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Hey, i am about to undertake an EPI at school in which i will be testing the spring constants of singular springs, and then of a few springs, both in parrallel and in series.

Before i start the prac i noticed that the equations for the overall spring constant of springs in series/parrallel are opposite to the equations for resistors in series/parrallel... i.e the equation for spring constant in series is the same as that for the resistors in parrallel.

What significance does this hold, if any?

Thanks for any input

-Spoon
 
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The formulas are similar because the mathematical behavior is the same. There are no physical similarities.

For two springs in parallel, the total force is the sum of each two forces. For resistors, the total current is the sum of the two currents. Formulas are similar, but you cannot assimilate forces to currents.
 
sorry I am not sure that i understand your explanation... if the sum of the forces in parrallel for a spring is just sprinbg one plus spring 2 etc... if the resistor equation works of the same principal would the equation for resistors in parrallel also be the resistance 1 plus resistance 2...it isn't however.. 1/R total = 1/R1 + 1/R2

Could you please try and explain again I am sorry i think i have just mis understood

Thanks

Spoon
 
In the case of two springs in parallel, when you stretch the two springs of the same amount (L) the total force will be:
Ft=F1+F2= Lk1+Lk2=Lkt
Then:
kt=k1+k2
For resistors, if a current I traverse the two resistors in series the voltage at the ends of two resistors will be:
Vt=V1+V2=IR1+IR2=IRt
Then:
Rt=R1+R2
You can do the same derivation imposing a force to two springs in series and imposing a voltage to two resistors in parallel.

The formulas are similar for (springs in parallel and resistors in series) and for (springs in series and resistors in parallel)

Same mathematical behavior does not mean physical similitude.
 
Last edited:
It works for capacitors too, if you reverse 'series' and 'parallel'.
 

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