Question

An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. Suppose that a typical car rounds the curve with a speed of 11.7m/s and that the radius of the curve is 50.0m. At what angle should the curve be banked?

Answer 1

To solve this problem we will make a graph that allows us to understand the components acting on the body. In this way we will have the centripetal Force and the Force by gravity generating a total component. If we take both forces and get the trigonometric ratio of the tangent we would have the angle is,

$T_x = nsinA = \frac{mv^2}{r}$

$T_y = ncosA = mg$

Dividing both.

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

$tan A = \frac{11.7^2}{50*9.8}$

$A = tan^{-1} (0.279367)$

$A = 15.608\°$

Therefore the angle that should the curve be banked is 15.608°