Uniform circular motion: A roadway for stunt drivers is designed for racecars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of 230 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?
A) 35°
B) 37°
C) 33°
D) 31°
E) 29°

Question

Quizplus · Accepted Answer

The formula for the angle of banking is given by:

$	heta = {	an ^{ - 1}}\left( {\frac{{{v^2}}}{{rg}}} ight)$

where $	heta$ is the angle of banking, $v$ is the speed of the car, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity.

Plugging in the given values, we get:

$	heta  = {	an ^{ - 1}}\left( {\frac{{{40^2}}}{{230 	imes 9.81}}} ight) = \boxed{35^\circ}$

Uniform Circular Motion: a Roadway for Stunt Drivers Is Designed