University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 5 - Applying Newton's Laws - Problems - Exercises: 5.48

Answer

(a) The minimum coefficient of static friction to prevent sliding is $\mu_s = 0.375$. (b) The maximum speed to round the curve safely is 14.4 m/s.

Work Step by Step

(a) In this situation, the force of static friction provides the centripetal force to go around the curve. $F_f = \frac{mv^2}{r}$ $mg~\mu_s = \frac{mv^2}{r}$ $\mu_s = \frac{v^2}{gr} = \frac{(25.0~m/s)^2}{(9.80~m/s^2)(170.0~m)}$ $\mu_s = 0.375$ The minimum coefficient of static friction to prevent sliding is $\mu_s = 0.375$. (b) Let $\mu_s = \frac{0.375}{3} = 0.125$ $mg~\mu_s = \frac{mv^2}{r}$ $v = \sqrt{gr~\mu_s}$ $v = \sqrt{(9.80~m/s^2)(170.0~m)(0.125)}$ $v = 14.4~m/s$ The maximum speed to round the curve safely is 14.4 m/s.
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