# A spring has a natural length of 26 centimeters. If a 23-Newton force is required to keep it...

## Question:

A spring has a natural length of 26 cm. If a 23-N force is required to keep it stretched to a length of 40 cm, how much work W is required to stretch it from 26 cm to 33 cm ?

## Work needed to Stretch the Spring:

To solve this problem we will use the following theorem:

Hooke's law: {eq}F = kx {/eq} where {eq}x {/eq} is the distance the spring is stretched from its natural length, and {eq}k {/eq} is the spring constant.

## Answer and Explanation:

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The spring's natural length is 26 cm. or 0.26 m., so it is stretched 14 cm. or 0.14 m.

Now, we can use:

{eq}W = \int dw = \int F \, dx =...

See full answer below.

#### Learn more about this topic: Hooke's Law & the Spring Constant: Definition & Equation

from

Chapter 4 / Lesson 19
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After 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.