Chapter 4, Problem 59P

To determine

What would be the magnitude of its deceleration if the road was inclined at 9.3° uphill?

Answer to Problem 59P

Solution:

Magnitude of deceleration=5.33m/s²

Explanation of Solution

Given:

a =-3.80m/s²

Formula used:

${\displaystyle \sum F=ma}$

Calculation:

$\begin{array}{l}\text{on level road,}\\ F_{fr}=\mu mg\\ ma=\mu mg\\ a=\mu g\\ \mu =\frac{a}{g}\\ \mu =\frac{-3.8}{-9.8}\\ \mu =0.3878\\ \text{when the car moves uphill}\\ mg\sin \theta +\mu mg\cos \theta =ma\\ a=g\sin \theta +\mu g\cos \theta \\ a=(-9.8)\sin 9.3+(0.3878)(-9.8)\cos 9.3\\ a=-5.33{\text{m/s}}^2\end{array}$