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 105: 64

Answer

The only safe driveway is the driveway with an incline of $6^{\circ}$.

Work Step by Step

We can use the force equation to find the maximum angle at which it is safe to park a car. Let's assume that the force of static friction $F_f$ directed up the slope is equal in magnitude to $mg ~sin(\theta)$ which is the component of the car's weight directed down the slope: $mg ~sin(\theta) = mg ~cos(\theta)\cdot ~\mu_s$ $tan(\theta) = \mu_s$ $\theta = tan^{-1}(\mu_s) = tan^{-1}(0.15) = 8.5^{\circ}$ The answer shows that the only safe driveway is the driveway with an incline of $6^{\circ}$ as the maximum safe angle is $8.5^{\circ}$. This means that the other two driveways are not safe because the incline is too large.
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