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?

Explanation:

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

- Vertical:

where

N is the normal reaction

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:

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:

In this problem:

(radius of the turn)

is the speed

Substituting, we find:

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