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Q.6

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 255

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Short Answer

A spring is compressed . How far must you compress a spring with twice the spring constant to store the same amount of energy?

Round off to two significant figures, the spring must be compressed to

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Step by Step Solution

Step 1: Introduction

The units for the spring constant are Newton per metre. We'll look at the spring constant definition now that we've established that k is the spring constant. The stiffness of the spring is defined as the spring constant.

Step 2: Explanation 

For the spring, the fresh spring energy is,

Here, is the new spring constant of the spring and is the compression of the spring. The new spring constant of the spring is,

Substitute for in the equation and solve for '.

Step 3: Explanation

Given that a spring with twice the spring constant stores the same amount of energy as a spring with half the spring constant.

Substitute for and for .

Now, solve for .

Round off to two significant figures, the spring must be compressed to .

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