Question

You need to design a banked curve at the new circular Super 100 Raceway. The radius of the track is 800 m and cars typically travel at speed 160 mi/h.What embankment angle should be to hold a car travelling at 160 mi/h if there were no friction between its wheels and the track?

Answer 1

Answer:

$33.1^{\circ}$

Explanation:

Let's start by writing the equations of the forces along the two directions:

- Vertical:

$N cos \theta = mg$

where

N is the normal reaction

$\theta$ is the angle between the road and the horizontal

(mg) is the weight of the car, with m being its mass and g the acceleration of gravity

- Horizontal:

$N sin\theta = m \frac{v^2}{r}$

where

v is the speed of the car

r is the radius of the turn

Dividing the 2nd equation by the 1st one, we get:

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

In this problem:

$r = 800 m$ (radius of the turn)

$v=160 mi/h = 71.5 m/s$ is the speed

$g=9.8 m/s^2$

Substituting, we find:

$\theta= tan^{-1} (\frac{v^2}{rg})=tan^{-1}(\frac{(71.5)^2}{(800)(9.8)})=33.1^{\circ}$