Effective Spring Constant of Springs in Series: Deriving & Explaining

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SUMMARY

The effective spring constant for two springs in series, denoted as k_eff, is derived using the formula k_eff = (k1 * k2) / (k1 + k2). This relationship is grounded in Hooke's Law, which states that the force exerted by a spring is proportional to its displacement (F = kx). The force acting on each spring remains constant due to Newton's Third Law, which asserts that the force exerted by one spring on another is equal and opposite, ensuring that the same force is transmitted through both springs.

PREREQUISITES
  • Understanding of Hooke's Law
  • Familiarity with Newton's Third Law of Motion
  • Basic knowledge of spring constants and their significance
  • Ability to manipulate algebraic equations
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  • Study the derivation of effective spring constants for springs in parallel
  • Explore applications of Hooke's Law in real-world scenarios
  • Learn about energy stored in springs and its relation to spring constants
  • Investigate the effects of damping on spring systems
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Students studying physics, particularly those focusing on mechanics and spring systems, as well as educators looking for clear explanations of spring behavior in series.

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Homework Statement


I am trying to derive the effective spring constant of two springs, with different spring constants, in series. I know the equation is everyone online, so the effective spring constant is k1k2/k1+k2.

So the question is, when deriving it, the force exerted on each spring is constant, why is that?? :confused:

Homework Equations


Hooke's Law -> Fx = kx

The Attempt at a Solution


Is it because of Newton's third law? If so, how does that work?? Force of mass on spring 2 is equal to force of spring 2 on spring 1? So the force acting on each spring is Fg??:confused:
 
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Hi Morass! :smile:
Morass said:
… Is it because of Newton's third law? If so, how does that work?? Force of mass on spring 2 is equal to force of spring 2 on spring 1?

Yes.
 

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