Formula for combined spring constant.

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SUMMARY

The formula for calculating the combined spring constant of two springs connected in series is derived from the relationship between tension and displacement. The correct formula is given by T = k_{series} (x_1 + x_2), where T is the tension, k_{series} is the combined spring constant, and x_1 and x_2 are the displacements of the individual springs. The relationship between the spring constants can be expressed as k_1 x_1 = k_2 x_2, indicating that both springs experience the same tension. Understanding these relationships is crucial for accurately determining the combined spring constant.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of mechanics and forces
  • Familiarity with algebraic manipulation of equations
  • Concept of tension in mechanical systems
NEXT STEPS
  • Research the derivation of the spring constant for springs in series
  • Explore the implications of cutting springs and how it affects spring constants
  • Learn about parallel spring configurations and their combined spring constants
  • Study practical applications of spring constants in engineering and physics
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Students studying physics, mechanical engineers, and anyone interested in understanding the mechanics of springs and their applications in real-world scenarios.

nerfed
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Help - Formula for combined spring constant.

Hey, I was wondering if anyone can help me with the formula to calculate the combined spring constant of two springs stuck together (end to end).

This is as far as I've been able to figure it out lol, I can't wrap my head around this formula. The k1 and x1 are the values of the first spring, and k2 and x2 are the values of the second spring respectively.

F(series) = [(k1)*(k2)] * [(x1)+(x2)]
 
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Not sure what that formula means. (The units don't make sense!)

Hint: Realize that two springs in series must have the same tension.
 
Heh, yeah, that's why I need the help.

I need to know how to find the spring constant of two springs connected end to end. That botched equation up there is my attempt at it, so I was wondering if you guys knew it.
 
You should be able to figure it out with the hint I gave. Use your same notation:
T = k_1 x_1 = k_2 x_2

But the tension is also given by:
T = k_{series} (x_1 + x_2)

Play around with these and see what you can do.
 
nerfed,

Here's another hint. If you have a spring with spring constant k and you cut it in two, what are the spring constants (call them k1 and k2) of the two pieces?
 

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