Combining springs to match Force vs Extension Graph

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SUMMARY

The discussion focuses on combining springs to achieve a specific force versus extension graph, utilizing Hooke's Law (F = -kx) and the equations for series and parallel spring combinations. The user calculated that to achieve an effective spring constant (k_eff) of 3/2, a combination of both parallel and series springs is necessary. Specifically, they proposed using five parallel springs in series with a single spring to meet the required k_eff. The logic presented aligns with the principles of spring mechanics, confirming the approach as valid.

PREREQUISITES
  • Understanding of Hooke's Law and its application in spring mechanics
  • Knowledge of series and parallel spring combinations
  • Ability to calculate effective spring constants (k_eff)
  • Familiarity with graph interpretation related to force and extension
NEXT STEPS
  • Study the derivation and applications of Hooke's Law in various contexts
  • Explore advanced spring combination techniques for complex systems
  • Learn about the practical applications of spring constants in engineering
  • Investigate graphical analysis methods for force vs. extension relationships
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Students in physics or engineering, mechanical engineers, and anyone involved in designing or analyzing spring systems and their behaviors under various forces.

srekai
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Homework Statement


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f

Homework Equations


Hooke's Law: F = -kx
Series spring combinations: ##\frac{1}{k_{eq}} = \frac{1}{k_1}+\frac{1}{k_2}##
Parallel spring combinations: ##k_{eq} = k_1+k_2##

The Attempt at a Solution


The slope of 1 is ##\frac{4}{5}## and the slope of 2 is ##\frac{3}{2}##

I calculated that we would need ##\frac{15}{8}## times of the original spring to produce the same amount of force. Unfortunately that's just less than 2, so I can't just make it a parallel set of 2 springs.
So I know that in order to get a k of ##\frac{3}{2}## it must be a combination of both parallel and series springs.

So I set it up as such ## \frac{3}{2} = \frac{1}{\frac{4}{5}} + \frac{1}{\text{some parallel combination of springs}}##

I get it so that it would be 5 parallel springs in series with a lone spring.
Does that logic sound correct? And the k_eff of the combination would just be ##\frac{3}{2}##?
 

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srekai said:
the slope of 2 is ##\frac{3}{2}##
Looks like a little more to me.
 
If you draw horizontal lines on the graph representing constant force, the extension for #2 looks to be about half #1.
 

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