Question

At what angle shall a curve be banked in order that a car with a velocity of 20.0 m/s will make the turn if the diameter of the path is 40.0 m?

Answer 1

Let's apply the Newton's Second Law of Motion in projections on $x$- and $y$-axis:

$$Nsin\theta=\dfrac{mv^2}{r},$$ $$Ncos\theta=mg.$$

Dividing the first equation by the second one, we get:

$$tan\theta=\dfrac{v^2}{gr},$$ $$\theta=tan^{-1}(\dfrac{v^2}{gr}),$$ $$\theta=tan^{-1}(\dfrac{(20\ \dfrac{m}{s})^2}{9.8\ \dfrac{m}{s^2}\times20\ m})=63.9^{\circ}.$$