Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 8 - Friction - Section 8.8 - Rolling Resistance - Problems - Page 454: 110



Work Step by Step

We know that $M=\frac{2}{3}(\frac{R_2^3-R_1^3}{R_2^2-R_1^2})$ $\implies M_A=\frac{2}{3}(0.20)(3000)[\frac{(0.03)^3-(0.01)^3}{(0.03)^2-(0.01)^2}]=13.00N.m$ Similarly $M_B=\frac{2}{3}(0.20)(1000)[\frac{(0.02)^3-(0.01)^3}{(0.02)^2-(0.01)^2}]=3.11N.m$ We also know that the sum of the moments about the z-axis is equal to zero $\implies \Sigma M_z=0$ $\implies M-M_A+M_B=0$ $\implies M=M_A+M_B$ $\implies M=13.00+3.11$ We plug in the known values to obtain: $M=16.11N.m$
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