Spring Constant and Deformation

[tigerwoods99]

Spring Constant and Deformation!

Homework Statement

If a spring with a constant K were to be cut in half, what would the spring constant be for each half?

Homework Equations

K = F/x, where F = force applied and x = length of the spring, or deformation.

The Attempt at a Solution

I have done some researching on the internet, and there is much disagreement about this topic. Some say the spring constant depends on the material and it will have the same constant no matter what lengh/demformation and others say that if the spring were to be cut in half, the spring constant would be double. (Which is what I believe)

Thanks! (I'am sure a lot of people are wondering this!)

 

[rogerbacon]

Imagine a spring suspended by its top with a weight of mass m, that is elongated by x.

You get |F|= mg = kx

Now while the spring is suspended by the top, take it with your fingers in the middle and lift it by a few mm (so that only half the spring is now suspended from the fingers). (Apologies for my bad English)

The lower part of the spring does not change. Before, the lower part of the spring was fixed to the upper part of the spring, now it is fixed to your fingers.

From that you can figure out the spring constant.

 

[tigerwoods99]

Yes, I fully know how to find spring constant. I was just wondering if the spring constant doubles if the spring is split into two halves. Or if the spring constant for a specific spring always stays the same, no matter what length.

Thanks.

 

[tigerwoods99]

Can someone please help me?

 

[tiny-tim]

Spring constant = force/displacement,

and force is the same all the way along a spring (like along a rope).

So … ? ​

 

[tigerwoods99]

"Now if you apply the same force to the half-length spring it only moves half as far. So if x is halved above, then k will double. Basically there are now half as many coils to take up the force via displacement."

Is that correct?

 

[tiny-tim]

Yup! (except I don't really understand the concept of "taking up the force").

 

[tigerwoods99]

Thanks! Though this makes sense as well, "Actually, I once asked my teacher what happens to the spring constant if a spring is cut in half and he said that the spring constant doesn't change because it depends on the material used to make the spring. It depends on the properties (molecular structure) of that material. One analogy he used is whether if you are boiling 1 liter of water or 50 liters, the boiling point is always 100 degrees Celsius."

 

[tiny-tim]

I suspect he was thinking of the elastic modulus.

Modulus is a property of material.

Spring constant is a type of stiffness, which is a property of a particular body (and btw, Young's "modulus" is a stiffness, not a modulus).

 

[tigerwoods99]

Thanks for all your help!

 

[Jmedz4nights]

Yeah, that spring constant cut in half is in my 1001 EK book. Basically, mechanically, to answer your question: k1x = k2x/2 => 2k1 = k2.