Question

An engineer wants to design an oval racetrack such that 3.20 × 10 3 lb racecars can round the exactly 1000 ft radius turns at 102 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h. Find the banking angle θ necessary for the race cars to navigate the turns at 102 mi/h without the aid of friction.

Answer 1

Answer:

The banking angle necessary for the race cars is 34.84°

Explanation:

For normal reaction the expression is:

$\\Nsin\theta = \frac{mv^{2} }{R} =Fc\\tan\theta =\frac{v^{2} }{Rg} \\\theta =tan^{-1} (\frac{v^{2} }{Rg} )\\\theta =tan^{-1} (\frac{(102*0.447)^{2} }{1000*0.3048*9.8} )=34.84$