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What is the spring factor? Find its value in case of two springs connected in
1. series
2. Parallel

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Last updated date: 23rd Jul 2024
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Answer
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Hint: A spring is a pliable object that can be used to store mechanical energy. Spring steel is the most common material used to make springs. There are several spring styles to choose from. Coil springs are often referred to as "coil springs" in ordinary use. When a typical spring is bent or extended from its resting state, it exerts an opposing force that is roughly equal to the length transition (this approximation breaks down for larger deflections).

Complete answer:
A spring's rate, or spring constant, is equal to the change in force it exerts divided by the change in deflection. That is, it is the force minus deflection curve's gradient. The rate of a compression or extension spring is measured in units of force separated by size.
The spring factor is the ratio of the force acting on the spring to the displacement of the spring. The letter k stands for it. Hooke's law is used to calculate it. It never changes (constant).
The spring factor is the force acting on the unit extension formed.
The stress exerted by both springs is the same when two springs are paired in series. The total extension (x) is equal to the number of the individual extensions.
\[ \Rightarrow {\text{X}} = {{\text{X}}_1} + {{\text{X}}_2}\]
\[\dfrac{F}{{ - {K_{eq}}}} = \dfrac{F}{{ - {K_1}}} + \dfrac{F}{{ - {K_2}}}\]
\[ \Rightarrow \dfrac{1}{{{{\text{K}}_{{\text{eq}}}}}} = \dfrac{1}{{{{\text{K}}_1}}} + \dfrac{1}{{{{\text{K}}_2}}}\]
\[{{\text{K}}_{{\text{eq}}}} = \dfrac{{{{\text{K}}_1}\;{{\text{K}}_2}}}{{\;{{\text{K}}_1} + {{\text{K}}_2}}}\]
When two springs are connected in a parallel configuration, the net force encountered is the sum of the forces experienced by both springs. The extension, though, will remain the same.
\[{{\text{F}}_{{\text{eq}}}} = {{\text{F}}_1} + {{\text{F}}_2}\]
\[{{\text{K}}_{{\text{eq}}}}X = {{\text{K}}_1}{\text{X}} + {{\text{K}}_2}{\text{X}}\]
\[ \Rightarrow {{\text{K}}_{{\text{eq}}}} = {{\text{K}}_1} + {{\text{K}}_2}\]

Note: The spring's force constant is determined by the material and construction of the spring. The minus sign denotes that the spring's momentum is in the opposite direction of its displacement.
Hooke's rule is usually followed by coil springs and other popular springs. There are some useful springs that do not: beam bending springs, for example, can create forces that differ nonlinearly with displacement.