Factors affecting the spring constant

In summary, the spring constant k of a spring is affected by factors such as the mass of a single atom, atomic spacing, bulk modulus, and density. However, it is usually determined empirically through measurement of forces and displacements rather than calculation. Additionally, cutting a spring in half will result in the spring constant doubling, as explained by Hooke's Law and the proportional relationship between force and extension.
  • #1
Corrupt Cannon
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Could anyone please tell me any factors affectin the spring constant k of a spring ?
 
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  • #2
I am not entirely sure if this is right, but I think I read somewhere that if you have a spring with spring constant [itex]k[/itex] and you cut it in half, the spring constant then doubles to [itex]2k.[/itex]

If that is true, can anyone please explain why this is the case?
 
  • #3
Welcome to the Forums both of you,

Corrupt Cannon; The spring constant is the constant of proportionality which appear in Hooke's Law; F = -kx. An alternative expression for Hooke's law is the strain is directly proportional to the stress placed on a object. From this we arrive at an approximation for the spring constant of a solid thus;

[tex] k = \frac{m}{a^2}\sqrt{\frac{K}{\rho}}[/tex]

Where [itex]m, a, K \& \rho[/itex] are the mass of a single atom, atomic spacing, bulk modulus and density respectively. However, it should be noted that values of k are determined empirically, i.e. by measurement and forces and displacements, rather than calculation.

CALCULATOR; Your statement is correct. Suppose we apply a force to a spring with 20 coils, this force results in an extension of 2cm. Therefore, each coil will have extended 0.2cm. Now, let us cut the spring in half, so we now have a new spring with 10 coils. Now suppose we exert a force such that an extension of 2cm is again produced, this means that each coil extends by 0.4cm. Now, according to Hooke's law F = -kx; the force required to extend the spring with 10 coils by 0.4cm is twice as large as the force required to extend the 20 coil spring by 0.2cm (since the extension in the smaller coils is twice that of the larger coil). It therefore follows that the spring constant of the smaller coil must be twice that of the larger coil (since force is proportional to extension).
 

1. What is the definition of spring constant?

The spring constant, also known as the force constant or stiffness, is a measure of the stiffness of a spring. It is defined as the amount of force required to stretch or compress a spring by a certain distance.

2. How does the material of a spring affect its spring constant?

The material of a spring can significantly affect its spring constant. Generally, stiffer materials such as steel have a higher spring constant, while more flexible materials like rubber have a lower spring constant.

3. How does the length of a spring affect its spring constant?

The length of a spring also affects its spring constant. In general, longer springs have a lower spring constant compared to shorter springs. This is because longer springs have more material to stretch, making them less stiff.

4. How does the diameter of a spring affect its spring constant?

The diameter of a spring can also impact its spring constant. A thicker spring will have a higher spring constant compared to a thinner spring, as it has more material to resist deformation.

5. How does the number of coils in a spring affect its spring constant?

The number of coils in a spring can affect its spring constant. Generally, a spring with more coils will have a higher spring constant. This is because more coils provide more material to resist deformation, making the spring stiffer.

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