# Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 320: 49

$1.6 \ J$

#### Work Step by Step

The work required to compress the spring beyond equilibrium can be calculated as: $\text{Work}, W= \int_{m}^{n} kx \ dx$; where $k$ is the spring constant. The spring constant is given by: $F=k x \implies 50 =0.05 k \\ k=1000 \ N/m$ Now, $W= \int_{m}^{n} kx \ dx\\= \int_{0.07}^{0.09} 1000 \ x \ dx\\=1000 [\dfrac{x^2}{2}]_{0.07}^{0.09} \\=(500) \times [(0.09)^2-(0.07)^2] \\=1.6 \ J$

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