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11CQ

Expert-verifiedFound in: Page 211

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 ** **.

A spring of spring constant K is cut in half.

**Two springs of the same material but having different lengths l _{1} and l_{2 }have their spring constants K_{1} and K_{2 }related as**

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

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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