Two Springs & Hooke's Law: Effect on Elastic Electrical Lead

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SUMMARY

This discussion focuses on the application of Hooke's Law in tensile testing of an elastic electrical lead encapsulated in elastic tubing. The primary inquiry revolves around the interaction of two springs with different spring constants (k values) when one is embedded within the other. The conclusion drawn is that the effective spring constant can be calculated using the formula F = k1X1 + k2X2, indicating that if both springs experience the same displacement, their constants can be summed to determine the overall stiffness. If one spring is significantly weaker, its contribution can be neglected without substantial error.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of tensile testing principles
  • Familiarity with elastic materials and their properties
  • Concept of effective spring constant in mechanical systems
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  • Research the mathematical derivation of Hooke's Law in composite spring systems
  • Explore the effects of material density on spring stiffness
  • Learn about tensile testing methodologies for biomedical applications
  • Investigate the implications of spring constants in mechanical design
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Engineers, materials scientists, and biomedical researchers involved in the design and testing of elastic components in medical devices will benefit from this discussion.

Laxbro112
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So I am doing tensile testing on an elastic electrical lead for biomedical purposes. The lead is encapsulated in an elastic tubing. Now the lead acts like a weak spring itself (coiled wire).
I'm curious, if there are two springs with different k constants "within" each-other (one inside the other) will it effect the Hooke's law equation? Or will the dominant k constant be the baseline?
 
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If you have two springs with the same k embedded into each other, what would happen? I think since the density of the spring is changed, you would have a greater stiffness. Would you use 2k and just add the two? If the springs were separate and working together you could assume that they work together.

Using
## F = k_1X_1 + k_2X_2 ##,
you can see that if the displacement is the same, the effective k is the sum of the two.

If the second is much weaker than the first, ignoring it will likely not induce a significant error.
 

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