Question

A curved road is banked at an angle such that friction is not necessary for a car to stay on the road. a 2500 kg car is traveling at a speed of 25 ms and the road has a radius of curvature equal to 40 m. calculate the magnitude of force that the road exerts on the car? I think that I need to use the F-mg=mv^2 equation but idk how we would put the angle in the equation.

Answer 1

force from road id perpendicular to road surface, call it N

N cos theta = m g

N sin theta = m v^2/R
so
tan theta = m v^2/( R m g) = v^2/(R g)
so
theta = tan^-1 (v^2/Rg)

N = m g /cos theta where theta = tan^-1(v^2/Rg)