A circular track of radius 600 m is to be designed for cars at an average speed of 180 km/hr. What should be the angle of banking of the track?
Let the angle of banking be θ. The forces on the car are
(a) weight of the car Mg downward and
(b) normal force N
For proper banking, static frictional force is not needed.
For vertical direction the acceleration is zero. So,
N cos θ = Mg ..........(i)
For horizontal direction, the acceleration is v2r towards the centre, so
N sin θ = Mv2r .......... (ii)
From (i) and (ii),
tan θ = v2rg
Putting the values, tan θ = (50 m/s)2(600 m)(10 m/s2) = 0.4167