Question

What is the maximum speed for a car rounding a 125 m curve on a highway under very icy (no friction) conditions if the banking angle is 20.0°.

Answer 1

N cos θ = m g where N is the normal force due to weight of car

N sin θ= m v^2 / R where N is portion of normal force providing centripetal acceleration

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

v^2 = 125 m * 9.80 m/sec^2 * .364 = 446 m^2 / s^2

v = 21.1 m/s max speed about 47.2 mph