Question

At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s^2 )

Answer 1

Answer:

Banking angle, $\theta=15.77^{\circ}$

Explanation:

It is given that,

Radius of the curve, r = 52 m

Speed of the car, v = 12 m/s

Acceleration due to gravity, $g=9.8\ m/s^2$

Let the curved is banked at an angle of $\theta$ with respect to the horizontal. It is given by :

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

$tan\theta=\dfrac{(12)^2}{52\times 9.8}$                

$\theta=15.77^{\circ}$

So, the curve is banked at an angle of 15.77 degrees wrt the horizontal. Hence, this is the required solution.