# Spring constant K question

#### physicsstudent12

if you cut a spring with a constant "k" in half, does the new spring's "k" change?

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#### H_man

What do you think would happen and why?

#### physicsstudent12

I'm not sure, I was thinking that the "k" would double, because by cutting the spring in half you are reducing the spring's displacement.

#### H_man

When you cut it in two you are not changing the displacement at all. That is, if by the displacement you mean how much you are compressing it.

#### physicsstudent12

okay, so now I'm really confused.
My other idea about the question was that maybe the "k" doesn't change at all, because it is a constant, so it is not effected by the change in the size of the spring.

#### FredGarvin

The units for the constant are in F/L where the L refers to the length of compression. Does it say anything about the spring's actual length?

#### physicsstudent12

Hey, Fred Garvin, thanks for replying, but there's nothing about the actual length of the spring. I don't need an exact numerical value, I just need to know if the spring constant changes, and if so, how does it change.

#### physicsstudent12

I think I found out the answer to my question. I think that k would be doubled, because the force of the spring is the same, and the length of compression is reduced. Can anybody tell me if that's right?

#### H_man

No

The spring constant does not change.

:rofl: :rofl:

#### FredGarvin

physicsstudent12 said:
Hey, Fred Garvin, thanks for replying, but there's nothing about the actual length of the spring. I don't need an exact numerical value, I just need to know if the spring constant changes, and if so, how does it change.
What I was trying to get at was that the spring constant is a function of material and the way it is wound. It is not a function of the overall length of the spring. The only thing that cutting a spring in half does is halves the total distance you can compress it before you reach the spring's solid height.

#### Q_Goest

Homework Helper
Gold Member
I'm not sure, I was thinking that the "k" would double, because by cutting the spring in half you are reducing the spring's displacement.
The tacit assumption I believe you're making is:
- This is in reference to a helically wound compression or extension spring.
- The spring is literally cut in half so that the material, wire diameter and coil diameter stay the same. Only the number of active coils gets reduced by 1/2.

If those are your assumptions, then you are correct. The k will double. The equation for spring constant for such a spring is:

k = d^4 * G / (8 * D^3 * N)

Where d = wire diameter
G = Modulus of rigidity
D = mean diameter of coil
N = Number of active coils

#### H_man

Thanks for that Q_Goest.

I always had thought it was just a function of the material and the way it was wound.

Sorry PhysicsStudent12 you were right all along

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