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Expert-verified Found in: Page 211 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # A certain uniform spring has spring constant. Now the spring is cut in half. What is the relationship between and the spring constant of each resulting smaller spring? Explain your reasoning.

When a spring of spring constant K is cut in half the spring constant of each of the resulting smaller springs is 2K .

See the step by step solution

## Step 1: Given data

A spring of spring constant K is cut in half.

## Step 2:Variation of spring constant

Two springs of the same material but having different lengths l1 and l2 have their spring constants K1 and K2 related as

$l{}_{1}{k}_{1}={l}_{2}{k}_{2}$

## Step 3: Determining the new spring constant when the length is halved

Let the initial length be L . Length of the new pieces when the spring is cut in half is L/2.

Thus from equation (I)

$Lk=\frac{L}{2}k\text{'}\phantom{\rule{0ex}{0ex}}k\text{'}=2k\phantom{\rule{0ex}{0ex}}$

Hence spring constant of each of the new pieces is2 K.

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