Question

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is frictionless?

Answer 1

Answer:

The road bank angle is 16.38⁰.

Explanation:

radius of curvature of the road, r = 50 m

allowable speed of car on the road, v = 12 m/s

The bank angle is calculated as;

$\theta = tan^{-1} (\frac{v^2}{gr} )$

where;

θ is the road bank angle

g is acceleration due to gravity = 9.8 m/s²

$\theta = tan^{-1} (\frac{v^2}{gr} )\\\\\theta = tan^{-1} (\frac{12^2}{9.8 \times 50} )\\\\\theta = tan^{-1} ( 0.2939)\\\\\theta = 16.38 ^0$

Therefore, the road bank angle is 16.38⁰.