# A spring has a free length of 70 mm. Calculate the work done (J) compressing a spring from an...

## Question:

A spring has a free length of 70 mm. Calculate the work done (J) compressing a spring from an initial length of 50 mm to a final length of 30 mm given a spring constant of k = 20 N/mm.

## Hooke's Law

The elastic force exerted by an ideal spring is described by Hooke's law,

{eq}\vec{F}=-k \Delta\vec{x} {/eq},

where {eq}k {/eq} is the elastic constant of the spring and {eq}\Delta \vec{x} {/eq} is the deformation vector. Note that the force always opposes the deformation while depending linearly on it. The elastic force is conservative, it has an associated potential energy,

{eq}E_{ep}=\dfrac{1}{2}k\Delta x^2 {/eq},

proportional to the squared deformation of the spring.

## Answer and Explanation:

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View this answerThe external agent performs work against the elastic force. Consequently, the work of the external agent opposes the work performed by the spring...

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Chapter 4 / Lesson 19After 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.