# If a 40 pound mass suspended on a spring scale stretches the spring 14 inches, how far will a 48...

## Question:

If a 40 pound mass suspended on a spring scale stretches the spring 14 inches, how far will a 48 pound mass stretch the spring?

## Hooke's Law:

Hooke's law states that the force applied on an elastic body is directly proportional to how much it can be stretched or compressed within a certain elastic limit, unique to the material. The proportionality constant is called the spring constant {eq}k. {/eq}

## Answer and Explanation: 1

There is a direct proportion to the force applied by the hanging mass and how much the spring is stretched. So if the spring is still within the elastic limit, the way the 40-lb mass is able to stretch the spring by 14 inches would be proportional to the length, {eq}x {/eq} a 48-lb mass would stretch the spring such that:

$$\begin{align} \dfrac {x}{48} &= \dfrac{14}{40} \\ x &= \dfrac {(14)(48)}{40} \\ x &= \dfrac {672}{40} \\ x &= 16.8 \rm \ inches \end{align} $$

The spring will be stretched by {eq}\color{blue}{16.8 \rm \ inches} {/eq} by the 48-lb mass.

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Chapter 4 / Lesson 19After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.