Question

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 194 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

Answer 1

Answer:

The banking angle is 23.84 degrees.

Explanation:

Given that,

Radius of the curve, r = 194 m

Speed of the car, v = 29 m/s

On the banked curve, the centripetal force is balanced by the force of friction such that,

$mg\ tan\theta=\dfrac{mv^2}{r}$

$tan\theta=\dfrac{v^2}{rg}$

$tan\theta=\dfrac{(29)^2}{194\times 9.8}$

$\theta=23.84^{\circ}$

So, the banking angle is 23.84 degrees. Hence, this is the required solution.