Question

If a roadway is banked at the proper angle, a car can round a corner without any assistance from friction between the tires and the road. Find the appropriate banking angle for a 900-kg car traveling at 20.5 m/s in a turn of radius 85.0 m.

Answer 1

N cos θ = m g where N is the normal force

N sin θ = m v^2 / R

tan θ = v^2 / (R g) dividing equations

tan θ = 20.5^2 / (85 * 9.80) = .505

θ = 26.8 deg banking angle required