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 = (mv^2)/(r)`

`T_y = ncosA = mg`

Dividing both.

`tan A = (v^2)/(rg)`

`tan A = (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°