Combining springs to match Force vs Extension Graph

In summary, the conversation discussed the use of Hooke's Law and series and parallel spring combinations to calculate the amount of force needed for a given slope. It was determined that a combination of both parallel and series springs would be necessary, with 5 parallel springs in series with a lone spring producing the desired slope and a k_eff of ##\frac{3}{2}##. However, further analysis revealed that the extension for #2 was actually slightly more than half of #1 on the graph.
  • #1
srekai
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0

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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  • #2
srekai said:
the slope of 2 is ##\frac{3}{2}##
Looks like a little more to me.
 
  • #3
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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