A spring has a spring constant "k" of 160\ \mathrm{N/m}. How much must this spring be compressed...

Question:

A spring has a spring constant "{eq}k {/eq}" of {eq}160\ \mathrm{N/m} {/eq}. How much must this spring be compressed (in meters) to store {eq}70\ \mathrm{J} {/eq} of energy?

Spring Constant:

It is the term that provides information about the relationship between the force applied and the deformation in the length of the spring. It is also stated as the fraction of the force employed on a spring to the variation in the length of the spring due to the application of load. If the deformation length of the spring increases its diameter reduces and vice versa.

Answer and Explanation: 1


Given data:

  • The spring constant is {eq}k = 160\;{\rm{N/m}}.{/eq}
  • The energy stored in spring is {eq}E = 70\;{\rm{J}}.{/eq}


The expression for the length of spring compressed during energy store is given as,

{eq}E = \dfrac{1}{2}k{x^2}{/eq}

Substitute values in the above expression.

{eq}\begin{align*} 70 &= \dfrac{1}{2} \times 160 \times {x^2}\\ x &\approx 0.94\;{\rm{m}} \end{align*} {/eq}


Thus, the length of spring compressed during energy store is {eq}0.94\;{\rm{m}}. {/eq}


Learn more about this topic:

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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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