Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

What is the spring constant of a spring that stores $25 J$ of elastic potential energy when compressed by $7 .5 cm$ ?

Spring constant is, $k = 8.9 \times 10^{3} N/m$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Elastic potential energy $U = 25 J$

Compressed length $x = 7.5 cm = 7.5 \times 10^{- 2} m$ .

Step 2: To understand the concept

The problem is based on the concept of elastic potential energy. It is energy stored as a result of applying a force to deform an elastic object. By using the concept of elastic potential energy, we can find the spring constant.

Formula:

$U = \frac{1}{2} k x^{2}$

Step 3: Calculate the spring constant of the spring

Elastic potential energy can be written as

$\begin{matrix} U = \frac{1}{2} k x^{2} \\ k = \frac{2 U}{x^{2}} \end{matrix}$

Substitute all the value in the above equation.

$\begin{matrix} k = \frac{2 \times 25 J}{{(7.5 \times 10^{- 2} m)}^{2}} \\ k = 8.9 \times 10^{3} N/m \end{matrix}$

Hence the spring constant is, $k = 8.9 \times 10^{3} N/m$ .

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Fundamentals Of Physics

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Short Answer

What is the spring constant of a spring that stores $25 J$ of elastic potential energy when compressed by $7 .5 cm$ ?

Step by Step Solution

Step 1: Given

Step 2: To understand the concept

Step 3: Calculate the spring constant of the spring

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Fundamentals Of Physics

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Short Answer

What is the spring constant of a spring that stores 25 Jof elastic potential energy when compressed by 7.5 cm?

Step by Step Solution

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Step 2: To understand the concept

Step 3: Calculate the spring constant of the spring

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What is the spring constant of a spring that stores $25 J$ of elastic potential energy when compressed by $7 .5 cm$ ?