Question

The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/s.

Hint:

The angle of banking ensures that a vehicle can safely navigate a curve without the need for frictional force to provide the centripetal force.

Answer 1

The angle of banking \( \theta \) for a car moving along a curved track without relying on friction is given by the formula:
\[ \tan(\theta) = \frac{v^2}{r g} \] where \( v = 25 \, {m/s} \) is the speed of the car, \( r = 200 \, {m} \) is the radius of the track, and \( g = 9.8 \, {m/s}^2 \) is the acceleration due to gravity. Substituting the values:
\[ \tan(\theta) = \frac{25^2}{200 \times 9.8} = \frac{625}{1960} = 0.318 \] \[ \theta = \tan^{-1}(0.318) = 17.7^\circ \]