# Suppose you had two flat rubber bands (A and B), identical in every way, but band A was 3x the...

## Question:

Suppose you had two flat rubber bands (A and B), identical in every way, but band A was 3x the width and 3x the thickness of band B. How would their Spring constants compare?

## Spring constant:

The spring constant of the material is inversely proportional to the length but directly proportional to the area of the cross-section that means the product of the thickness and the width of the object.

Given Data:

• Width of the band A {eq}\rm (w_{A}) = 3b {/eq}
• thickness of band A {eq}\rm (t_{A}) = 3t {/eq}
• width of the band B {eq}\rm (w_{B}) = b {/eq}
• thickness of the band B {eq}\rm (t_{B}) = t {/eq}

Now, the spring constant can be given as

{eq}\rm \dfrac{k_{A}}{k_{B}} = \dfrac{w_{A}t_{A}}{w_{B}t_{B}} \\ \dfrac{k_{A}}{k_{B}} = \dfrac{3b \times 3t}{bt} \\ \dfrac{k_{A}}{k_{B}} = 9 {/eq}

Hence the spring constant of the band A is 9 times that of the band B.

Practice Applying Spring Constant Formulas

from

Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.