Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 320: 48


$1.08 \ J$

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. and $\dfrac{1}{2} k(0.2)^2=12 \implies k =600 \ N/m$ Now, $W= \int_{m}^{n} kx \ dx\\= \int_{0}^{0.06} 600 \ x \ dx\\=600 [\dfrac{x^2}{2}]_{0}^{0.06} \\=(600) \times [\dfrac{(0.06)^2}{2}] \\=1.08 \ J$
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