Physics: Principles with Applications (7th Edition)

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

Chapter 4 - Dynamics: Newton's Laws of Motion - Problems - Page 103: 31

Answer

(a) $\theta = 23^{\circ}$ (b) The angle is toward the windshield.

Work Step by Step

(a) First let's find the acceleration. $a = \frac{v-v_0}{t} = \frac{0-25 ~m/s}{6.0 ~s} = -4.2 ~m/s^2$ The magnitude of acceleration is $a = 4.2 ~m/s^2$. We can use the acceleration to find the angle. $F_T ~sin(\theta) = ma$ $F_T ~cos(\theta) = mg$ Let's divide the first equation by the second equation. $tan(\theta) = \frac{a}{g}$ $\theta = tan^{-1}(\frac{a}{g}) = tan^{-1}\frac{4.2 ~m/s^2}{9.80 ~m/s^2} = 23^{\circ}$ (b) The angle is toward the windshield. The car is decelerating, so the horizontal component of the tension is pulling the object backward. Therefore the angle must be toward the windshield.
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