Question

Does diameter affect spring constant?

Answer 1

When attempting questions based on spring constant, keep in mind various concepts regarding the factors which can affect spring constant; which can make it increase or decrease. Keep in mind the various other concepts regarding spring constant and where they are applied.

Complete step by step answer:
Before we get into solving this question, let’s keep in mind what spring constant actually is.
Spring constant is a constant or term which is often used in Hooke’s law, which states that a particular force ($F$) is needed to extend or compress a spring by some specified distance ($x$) which when scaled linearly with respect to that distance comes out to be
$\Rightarrow {{F}_{s}}=kx$
Where $k$is the constant factor and is known as the spring factor.
The modern theory of Hooke’s law states that the strain or deformation of any elastic object is proportional to the stress applied to it, but it usually doesn’t work because general stress and strain can have multiple independent components, and hence the proportionality factor may not work as a single real number
In simple terms we can say that spring constant is the force applied to an object if the displacement in the spring is unity.
There are multiple factors which can determine the spring constant, and diameter plays an important role in it. Firstly the material itself is a factor to determine the spring constant value. For example if we have steel and brass the spring constant for both will be different because both are different materials and spring constant depends on material to material. Secondly we have the diameter.
If the diameter is large the spring will be stiffer, because spring constant is inversely proportional to diameter of coil. With an increase in diameter of the spring the spring constant will decrease.
So hence we can conclude by saying that Yes, diameter does affect the spring constant.

Note:
Another factor to keep in mind regarding Spring constant is length and number of coils per unit length. Spring constant is a feature mostly concerning the spring, but it can be determined by applying a known force and by measuring the extension or compression caused by the force on the known mass.