Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 8 - Dynamics II: Motion in a Plane - Exercises and Problems: 40

Answer

The net force on the rotor is 64.5 N

Work Step by Step

We first convert 70,000 rpm to units of rad/s; $\omega = (70,000~rpm)(\frac{2\pi~rad}{1~rev})(\frac{1~min}{60~s})$ $\omega = 7330.4~rad/s$ We can assume that the masses of the two samples are $m$ and $(m+10\times 10^{-6}~kg)$. We can find the magnitude of the net force on the rotor. Let $a_c$ be the centripetal acceleration. $\sum F = (m+10\times 10^{-6}~kg)~a_c-m~a_c$ $\sum F = (10\times 10^{-6}~kg)~a_c$ $\sum F = (10\times 10^{-6}~kg)(\omega^2~r)$ $\sum F = (10\times 10^{-6}~kg)(7330.4~rad/s)^2(0.12~m)$ $\sum F = 64.5~N$ The net force on the rotor is 64.5 N.
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