An engineer must design a curved exit ramp for a highway in such a way that a ca
ID: 2093993 • Letter: A
Question
An engineer must design a curved exit ramp for a highway in such a way that a car, exiting at the posted speed limit of 17.88 m/s (40 mi/hr), does not depend on friction to round the curve without skidding. The radius of the curve is 225.0 m. At what angle with respect to the horizontal must the curve be banked (in degrees)?
No friction will be needed if the centripetal force on the car rounding the ramp exactly equals the total horizontal force on the car. The force of gravity acts straight down so the only force that has a horizontal component is the normal force.
Explanation / Answer
Ncos(theta) = mg
and Nsin(theta) = mv^2/r
divide eqtn 2 by eqtn 1 ,
tan(theta) = 17.88^2 / 9.81 x 225 = 0.145
theta = tan^-1(-.145) = 8.24 degrees