- #1
physicsstudent12
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if you cut a spring with a constant "k" in half, does the new spring's "k" change?
Does Cutting a Spring in Half Change Its Spring Constant K?
- Thread starter physicsstudent12
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In summary, the spring constant, denoted by "k", is a function of the material and the way the spring is wound. Cutting a spring in half does not change the value of "k", as it is not affected by the overall length of the spring. However, the spring's displacement is reduced by half, which may lead to the misunderstanding that "k" would double. Additionally, the equation for calculating "k" for a helically wound compression or extension spring is k = d^4 * G / (8 * D^3 * N), where d is the wire diameter, G is the modulus of rigidity, D is the mean diameter of the coil, and N is the number of active coils.
- #2
H_man
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What do you think would happen and why?
- #3
physicsstudent12
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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.
- #4
H_man
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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.
- #5
physicsstudent12
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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.
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.
- #6
FredGarvin
Science Advisor
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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?
- #7
physicsstudent12
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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.
- #8
physicsstudent12
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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?
- #9
H_man
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No
The spring constant does not change.
The spring constant does not change.
- #10
FredGarvin
Science Advisor
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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.physicsstudent12 said:
- #11
Q_Goest
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Homework Helper
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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
- #12
H_man
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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
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
FAQ: Does Cutting a Spring in Half Change Its Spring Constant K?
1. What is the spring constant K?
The spring constant K, also known as the force constant or stiffness coefficient, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.
2. How is the spring constant K calculated?
The spring constant K is calculated by dividing the force applied to a spring by the distance the spring is stretched or compressed. This can be expressed in the equation K = F/x, where K is the spring constant, F is the force applied, and x is the distance the spring is stretched or compressed.
3. What are the units for the spring constant K?
The units for the spring constant K depend on the units used for force and distance in the calculation. In the SI system, the units for K are N/m (newtons per meter).
4. How does the spring constant K affect the behavior of a spring?
The spring constant K determines how stiff or flexible a spring is. A higher K value indicates a stiffer spring, which requires more force to stretch or compress. A lower K value indicates a more flexible spring, which requires less force to stretch or compress.
5. Can the spring constant K change?
Yes, the spring constant K can change depending on factors such as the material and dimensions of the spring, as well as external factors such as temperature and applied force. However, for a specific spring, the spring constant K remains constant as long as the spring is not permanently deformed.