Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 8 - Rotational Motion - General Problems - Page 228: 96

Answer

a) $\Delta x=1.52m$ b) $\Delta x=2.14m$

Work Step by Step

$r=0.076m$ $I=3.3\times10^{-3}kgm^2$ $I=\frac{MR^2}{2}=\frac{(m)(0.076m)^2}{2}=3.3\times10^{-3}kgm^2$ $m=1.143kg$ a) $F_f=\frac{\tau}{r}=1.45N$ $a=\frac{F_p-F_f}{m}=\frac{3.5N-1.45N}{1.143kg}=1.79\frac{m}{s^2}$ $v_i=0\frac{m}{s}$ $t=1.3s$ $\Delta x=v_it+\frac{at^2}{2}=1.52m$ $v_f=v_i+at=2.33\frac{m}{s}$ b) $v_i=2.33\frac{m}{s}$ $v_f=0\frac{m}{s}$ $a=\frac{F_f}{m}=1.27\frac{m}{s^2}$ $v_f^2=v_i^2+2a\Delta x$ $\Delta x=\frac{v_f^2-v_i^2}{2a}=2.14m$
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