Question

What is the angle of banking for a curve road radius 180m suitable for a maximum speed of 30m? Calculate the maximum speed to be maintained when the angle of banking is θ = 30° (g = 9.8ms^-1)

Answer 1

Radius of the curve road, r =180m, Maximum speed v=30 ms^-1 Angle of banking 0 =? Acceleration due to gravity, g = 9.8 ms^-2 From the equation,

tan θ = \(\frac{v^2}{rg}\) 

= \(\frac{30^2}{180\times \,9.8}\)

= \(\frac {900}{1764}\)

= 0.5102

θ = tan^-1 (0.5102)

= 27°

When the angle of banking θ = 30°

From the equation tan θ = \(\frac {v^2}{rg}\)

tan θ 30° = \(\frac {v^2}{180 \times \,9.8}\)

v² = 180 × 9.8 × tan 30°

= 1764 × 0.5774 = 1018.5

v = 32 ms^-1.