College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 4 - Problems - Page 152: 71


(a) $t = 7.69~s$ The minimum coefficient of friction is $1.38$ (b) $t = ~9.20s$

Work Step by Step

(a) We can find the acceleration: $v_f^2 = v_0^2+2ad$ $a = \frac{v_f^2-v_0^2}{2d}$ $a = \frac{(104~m/s)^2-0}{(2)(400.0~m)}$ $a = 13.52~m/s^2$ We can find the time to complete the race: $v_f = v_0+at$ $t = \frac{v_f-v_0}{a}$ $t = \frac{104~m/s-0}{13.52~m/s^2}$ $t = 7.69~s$ We can find the minimum coefficient of static friction: $mg~\mu_s = ma$ $\mu_s = \frac{a}{g}$ $\mu_s = \frac{13.52~m/s^2}{9.80~m/s^2}$ $\mu_s = 1.38$ (b) We can find the new acceleration: $a = 0.70~a_0 = (0.70)(13.52~m/s^2) = 9.46~m/s^2$ We can find the time to complete the race: $d = \frac{1}{2}at^2$ $t = \sqrt{\frac{2d}{a}}$ $t = \sqrt{\frac{(2)(400.0~m)}{9.46~m/s^2}}$ $t = ~9.20s$
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