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 15.64 m/s (35 mi/hr), does not depend on friction to round the curve without skidding. The radius of the curve is 182.0 m. At what angle with respect to the horizontal must the curve be banked (in degrees) ?

Question

Physics

Lorena Heath

21 March, 09:11

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 15.64 m/s (35 mi/hr), does not depend on friction to round the curve without skidding. The radius of the curve is 182.0 m. At what angle with respect to the horizontal must the curve be banked (in degrees) ?

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Aisha Malone · Answer 1

The centripetal force on the car must be equivalent to the car's weight component. This is:

mv²/r = mgsin (∅)

We are left with:

v²/r = gsin (∅)

∅ = sin⁻¹ (15.64² / (182 x 9.81))

∅ = 7.87°