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Q1P

Expert-verifiedFound in: Page 202

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**What is the spring constant of a spring that stores **** ${\mathbf{25}}{\mathbf{\text{\xe2\u20ac\u2030J}}}$of elastic potential energy when compressed by ${\mathbf{7}}{\mathbf{.5}}{\mathbf{\text{\xe2\u20ac\u2030cm}}}$****?**

** **

Spring constant is,$k=8.9\xc3\u2014{10}^{3}\text{\xe2\u20ac\u2030N/m}$ .

Elastic potential energy$U=25\text{\xe2\u20ac\u2030J}$

Compressed length$x=7.5\text{\xe2\u20ac\u2030cm}=7.5\xc3\u2014{10}^{\xe2\u02c6\u20192}\text{\xe2\u20ac\u2030m}$ .

**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:**

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

Elastic potential energy can be written as

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

Substitute all the value in the above equation.

$\begin{array}{c}k=\frac{2\xc3\u201425\text{\xe2\u20ac\u2030J}}{{(7.5\xc3\u2014{10}^{\xe2\u02c6\u20192}\text{\xe2\u20ac\u2030m})}^{2}}\\ k=8.9\xc3\u2014{10}^{3}\text{\xe2\u20ac\u2030N/m}\end{array}$

Hence the spring constant is, $k=8.9\xc3\u2014{10}^{3}\text{\xe2\u20ac\u2030N/m}$.

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