Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 11 - Rolling, Torque, and Angular Momentum - Problems - Page 320: 1e

Answer

Relative to the woman, the magnitude of the acceleration at the top of the tire is $1500~m/s^2$

Work Step by Step

We can convert the speed of the car into units of $m/s$: $v = (80~km/h)\times (\frac{1000~m}{1~km})\times (\frac{1~h}{3600~s}) = 22~m/s$ The velocity of the tire's center of mass is equal to the velocity of the car. Since the car is moving at a constant velocity, the acceleration of the woman is zero, and the acceleration at the center of the tire is zero. At the top of the tire, there is a centripetal acceleration directed toward the center of the tire. We can find the magnitude of this acceleration: $a = \frac{v^2}{r}$ $a = \frac{(22~m/s)^2}{0.33~m}$ $a = 1500~m/s^2$ The magnitude of the acceleration at the top of the tire relative to the woman is $(1500~m/s^2-0)$ which is $1500~m/s^2$ Relative to the woman, the magnitude of the acceleration at the top of the tire is $1500~m/s^2$
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