A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. what is the appropriate banking angle so that the car stays on its path without the assistance of friction

The centripetal force tending to take the car off track is

[ (600 kg) (24.5 m/s) ^2] / (110 m) = 3274.09 N

Let the banking angle be x.

Then the restorative force on the car is

(600 kg) (9.8 m/s^2) sin (x) = 5880sin (x) N

For dynamic equilibrium,

5880sin (x) = 3274.09

sin (x) = 0.5568

x = arcsin (0.5568) = 33.8°

Answer: 33.8°