Answer to Question #159246 in Mechanics | Relativity for Max

Question

Write the note on spring constant

Answer 1

Explanation

• It is the proportionality constant of Hook's law that is described for the regainable deformation of spring and written as $\small F= kx$, $\small k: \text{the spring constant}$.
• Dimension can be found as

$\qquad\qquad \begin{aligned} \small [k]&=\small \frac{[F]}{[x]}=\frac{MLT^{-2}}{L}=MT^{-2} \end{aligned}$

• Unit is commonly written as $\small Nm^{-1}$
• Stiffness of a spring increases as the string constant increases & vice-versa.
• It is unique to a given spring & varies between springs with the dimension & the material they are made of.
• This can be understood by comparing it with the general explanation to the elastic behavior of matter which is written as $\small \sigma=E\epsilon \to \large \frac{F}{A} \small =Y\large\frac{e}{L}\small\to F=\large \frac{AY}{L}\small \implies k=\large \frac{AY}{L}$
• This form is applicable for all the solid substances within their proportionality limits but the name "spring constant" is usually used for springs only as for a given spring it is constant & noo need of describing the behavior in terms of A, Y or L