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 road way is icy (and the frictional force is zero)

The banking angle of the road is 16.38 degrees.

Explanation:

Given:

Radius of the roadway on curve, R = 50 m

velocity of the moving car, V = 12 m/s

The banking angle can be calculated by using the formula below:

If there's no frictional force, then net force is equal to centripetal force.

MgTanΦ = (MV^2) / R

TanΦ = V^2 / gR

Where;

Φ is the banking angle

g is acceleration due to gravity

TanΦ = (12 x 12) / (9.8 x 50)

TanΦ = 0.2939

Φ = arctan (0.2939)

Φ = 16.38 degrees

Therefore, the banking angle of the road is 16.38 degrees.