Answered: A sport car is traveling along a 10°…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A sport car is traveling along a 10° banked road having a radius of curvature of 136 ft.

The driver wants to increase his speed to 83 ft/s and wants to know which tires he must select.

Determine (with 2 digits after the decimal point) the minimal required static friction between the tires and the road

Expert Solution

Step 1

To Find-:

The minimal required static friction between the tires and the road.

Given-:

The angle of banked road is $θ = 10^{o}$ .

The radius of curvature is $R = 136 f t$ .

The speed of the car is $V = 83 \frac{f t}{s}$ .

Concept used-:

The minimal static friction is required that means the formula for maximum velocity achieved on a banked road by the car must be considered.

Formula used-:

The expression for maximum speed on a banked road is-:

$\begin{array}{rcl} V & = & \sqrt{\frac{R g (\sin θ + μ \cos θ)}{\cos θ - μ \sin θ}} \end{array}$ (1)

Calculations-:

Substitute the value of $R = 136 f t$ , $θ = 10^{o}$ , $V = 83 \frac{f t}{s}$ and $g = 32.2 \frac{f t}{s^{2}}$ in equation (1).

$\begin{array}{rcl} 83 & = & \sqrt{\frac{136 \times 32.2 \times (\sin 10^{o} + μ \cos 10^{o})}{\cos 10^{o} - μ \sin 10^{o}}} \\ {(83)}^{2} & = & \frac{136 \times 32.2 \times (\sin 10^{o} + μ \cos 10^{o})}{\cos 10^{o} - μ \sin 10^{o}} \\ 6889 \times (\cos 10^{o} - μ \sin 10^{o}) & = & 4379.2 \times (\sin 10^{o} + μ \cos 10^{o}) \\ 6784.34 - 1196.26 μ & = & 760.44 + 4312.67 μ \\ 5508.9 μ & = & 6023.9 \\ μ & = & 1.09 \end{array}$

Thus, the value of the minimal required static friction between the tires and the road is $μ = 1.09$ .

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