Spring Constants: Does Changing Diameter Affect Constant?

In summary, the spring constant is determined by the mass applied and the vertical displacement. The change in number of coils would change the length of the spring, but I am not sure if this would affect the stiffness.
  • #1
simplyphysics
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Homework Statement


If you change the diameter of a spring does it affect the spring constant? Assume the spring length, if fully extended, was kept constant.

Homework Equations


F=kx; F=mg

The Attempt at a Solution


From my research the spring constant (k) is measured by applying a mass and determining the vertical displacement (x) of the spring. The spring force is just equal but opposite to that of the force of gravity. Using Hooke's law the spring constant of a specific spring can be determined.
I know that the spring constant tells us the stiffness of the spring. I'm not sure how this would change if we were to use the same spring, unravelling it and then creating a larger diameter but lowering the number of coils. I think this would be difficult to test experimentally as the spring state would definitely be compromised. For some reason my mind is fuzzing out and I cannot think of whether changing the number of coils would affect the spring constant or stretch. I think maybe the spring would not stretch as far, keeping the mass applied the same, the spring constants would be different...but I'm still not sure. Help?
 
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  • #2
You may need to think about how a spring works. Consider a very short section of the wire. As the load is applied, what deformation (primarily) occurs?
 
  • #3
k = Gd4/[8nD3]

Where:

k = constant, pounds of load per inch of deflection
G = modulus of rigidity of spring material, pounds per square inch
d = wire diameter, inches
n = number of active coils, which is the number of coils subjected to flexure (always less than the total number of coils)
D = mean coil diameter, inches = Outer Diameter - Wire Diameter
 
  • #4
Don't springs work on the concept of shearing stress -rigidity modulus?
changing the number of coils would change the natural length of the spring.
αR=θL
so required shear angle = θ
θ α R/L
and also F/A α θ
I don't know if this is even right!
Sorry if this could not help you.
 
  • #5


I would approach this question by first understanding the concept of the spring constant. The spring constant is a measure of the spring's stiffness and is defined as the force required to stretch or compress the spring by a certain distance. It is a characteristic property of the spring and is not affected by external factors such as the mass or length of the spring.

In this case, changing the diameter of the spring would not directly affect the spring constant. This is because the spring constant is determined by the material and geometry of the spring, not its size or shape. However, changing the diameter of the spring may indirectly affect the spring constant by altering its length and number of coils.

If the spring length is kept constant, changing the diameter of the spring would affect the number of coils. A larger diameter would result in fewer coils, while a smaller diameter would result in more coils. This change in the number of coils would impact the overall length of the spring and therefore its stiffness.

To determine the effect of changing the diameter on the spring constant, a controlled experiment could be conducted by measuring the displacement of the spring for a given mass with different diameters and keeping the length of the spring constant. This would provide data to analyze and determine if there is a correlation between the diameter of the spring and its spring constant.

In conclusion, changing the diameter of a spring may indirectly affect its spring constant by altering its length and number of coils. However, the spring constant itself is a characteristic property of the spring and is not directly affected by changes in diameter.
 

1. How does changing the diameter affect the spring constant?

Changing the diameter of a spring does not directly affect its spring constant. The spring constant, or stiffness, is determined by the material and geometry of the spring, not its diameter.

2. Will increasing the diameter of a spring increase its spring constant?

No, increasing the diameter of a spring will not necessarily increase its spring constant. As mentioned before, the spring constant is determined by other factors such as material and geometry.

3. Does increasing the diameter of a spring make it more or less stiff?

Increasing the diameter of a spring will make it more stiff. This is because a larger diameter means there is more material and a larger cross-sectional area, which leads to a higher spring constant.

4. Is there a limit to how much the diameter of a spring can be changed before it affects the spring constant?

There is no specific limit to how much the diameter of a spring can be changed before it affects the spring constant. However, if the diameter is changed significantly, the spring may no longer function as intended and may not have a predictable spring constant.

5. Can the spring constant be calculated if the diameter is changed?

Yes, the spring constant can still be calculated if the diameter is changed. The formula for calculating spring constant takes into account the diameter, but as mentioned before, the diameter is not the only factor that affects the spring constant.

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