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
8
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.
 

1. How can I combine multiple springs to match a desired Force vs Extension graph?

To combine springs to match a desired Force vs Extension graph, you will need to first calculate the spring constant for each individual spring. Then, add up the individual spring constants to get the total spring constant. Finally, use this total spring constant to calculate the equivalent spring stiffness for the combined springs.

2. What is the formula for calculating the spring constant?

The formula for calculating the spring constant is F = kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring.

3. Can I combine springs with different spring constants?

Yes, you can combine springs with different spring constants. However, the resulting combined spring will have a different spring constant than any of the individual springs. You will need to calculate the equivalent spring stiffness for the combined springs to determine the new spring constant.

4. How do I determine the force and extension values for each individual spring?

To determine the force and extension values for each individual spring, you will need to conduct experiments where you apply known forces and measure the corresponding extensions for each spring. This will allow you to create a Force vs Extension graph for each spring.

5. Is there a limit to the number of springs that can be combined?

There is no limit to the number of springs that can be combined. However, as you add more springs, the resulting combined spring will have a higher spring constant and will require more force to extend. Additionally, there may be practical limitations depending on the specific setup and materials being used.

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