Question

A curve along the highway is to be designed for cars moving at 100 kilometers per hour. Find the angle of banking if the radius of the curve is 200 m.

Answer 1

Let's apply the Newton's Second Law of Motion:

$$Ncos\theta=mg, (1)$$ $$Nsin\theta=\dfrac{mv^2}{r}. (2)$$

Dividing equation (2) by equation (1), we get:

$$tan\theta=\dfrac{v^2}{gr},$$ $$\theta=tan^{-1}(\dfrac{v^2}{gr}),$$ $$\theta=tan^{-1}(\dfrac{(100\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s})^2}{9.8\ \dfrac{m}{s^2}\cdot200\ m})=21.5^{\circ}.$$