Question

Highway curves are often banked to reduce a vehicle’s reliance on friction when negotiating the turn: On a banked curve, there is a centripetal component of normal force acting on the vehicle.When the angle and speed are such that friction plays no role in a vehicle’s motion in the curve, the nature of the road surface is immaterial and thus the posted speed limit applies in both wet and dry weather. Suppose the posted speed limit is 100 km/h on a curve of radius 180 m. At what angle θto the horizontal should the curve be banked so that reliance on friction is not necessary?

Answer 1

The maximum speed of a vehicle on a banked road without taking friction between tyre and road is called optimum speed(v).

optimum speed(v)=rgtan

v=100km/h=100x5/18m/s=27.8m/s

where r= radius of curved road=180m

g=acceleration due to gravity=9.8m/s2

=angle of banking=?

v=rgtan

27.8 =180x9.8xtan

squaring

27.82 =180x9.8xtan

tan=27.82 /180x9.8

tan =0.438

Hence =tan-1(.438)

=23.70