Chapter 4, Problem 62P

On an icy day, you worry about parking your car in your driveway, which has an incline of 12°. Your neighbor's driveway has an incline of 9.0°, and the driveway across the street is at 6.0°. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?

To determine

On an icy day, you worry about parking your car in your driveway which has an incline of ${12}^{\circ }$. Your neighbor’s driveway has an incline of $9^{\circ }$, and the driveway across the street is at $6^{\circ }$. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s)will be safe to park in?

Answer to Problem 62P

Solution:

Only the driveway across the street is safe.

Explanation of Solution

Given:

$\begin{array}{l}{\theta }_1={12}^{\circ }\\ {\theta }_2=9^{\circ }\\ {\theta }_3=6^{\circ }\\ {\mu }_k=0.15\end{array}$

Formula used:

${\displaystyle \sum F=ma}$

Calculation:

$\begin{array}{l}\text{for the incline}\\ mg\sin \theta -{\mu }_{k}mg\cos \theta =ma\\ a=0\\ mg\sin \theta -{\mu }_{k}mg\cos \theta =m(0)\\ mg\sin \theta ={\mu }_{k}mg\cos \theta \\ {\mu }_k=\frac{\sin \theta }{\cos \theta }\\ {\mu }_k=\tan \theta \\ \theta ={\tan }^{-1}({\mu }_k)\\ \theta ={\tan }^{-1}(0.15)\\ \theta ={8.53}^{\text{o}}\\ \text{The car will start sliding if the angle of incline is equal to or greater than 8}{\text{.53}}^{\text{0}}\text{.So only the driveway}\\ {\text{ across the street(6}}^{\text{o}}\text{) is safe}.\end{array}$