A spring has a natural length of 12 cm. If a 29-N force is required to keep it stretched to a...

Question:

A spring has a natural length of 12 cm. If a 29-N force is required to keep it stretched to a length of 18 cm, how much work is required to stretch it from 12 cm to 15 cm?

Hooke's Law & the Spring Constant:

According to Hooke's Law {eq}F~\alpha ~x~~or ~~F=kx {/eq} which states that force applied on the spring to compress or expand is directly proportional to the length compressed or stretched respectively. Here {eq}k {/eq} is called spring constant. Also the work done is found using the formula: {eq}WD=\int_{a}^{b} k x dx {/eq}

Answer and Explanation:

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We are given with :

{eq}F= 29~ N ~and ~x = (0.18-0.12) = 0.06~ meter {/eq}

Now {eq}k=\frac{F}{x}\\ k=\frac{29}{0.06}\\ k=483.34...

See full answer below.


Learn more about this topic:

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Hooke's Law & the Spring Constant: Definition & Equation

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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.


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