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

The road bank angle is 16.38⁰.

Step-by-step 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) ((v^2)/(gr) )`

where;

θ is the road bank angle

g is acceleration due to gravity = 9.8 m/s²

`\theta = tan^(-1) ((v^2)/(gr) )\\\\\theta = tan^(-1) ((12^2)/(9.8 * 50) )\\\\\theta = tan^(-1) ( 0.2939)\\\\\theta = 16.38 ^0`

Therefore, the road bank angle is 16.38⁰.