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An engineer must design a curved exit ramp for a highway in such a way that...

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 230 m. At what angle with respect to the horizontal must the curve be banked (in degrees)?

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Answer #1

in this case,

Ncos(theta) = mg

the centripetal force is balanced by

Nsin(theta) = mv^2/r

divide eqtn 2 by eqtn 1 ,

tan(theta) = (mv^2/r)/(mg)

=(17.88)^2 / (9.81 x 230)

= 0.142

theta = tan^-1(-.142) = 8.06 degree

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