Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 15 - Oscillations - Problems: 73a

Answer

$k=130N/m$

Work Step by Step

To find the spring constant, use Hooke's law. Since all forces must add up to zero, it can be concluded that if $F_s=-k\Delta x$, $$mg+k\Delta x=0$$ $$mg=-k\Delta x$$ Solving for $k$ yields $$k=-\frac{mg}{\Delta x}$$ Substituting known values of $\Delta x=9.6cm=0.096m$, $m=1.3kg$, and $g=-9.8m/s^2$ yields a spring constant of $$k=-\frac{(1.3kg)(-9.8m/s^2)}{0.096m}$$ $$k=130N/m$$
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