Banked Curves Practice Problems
A 1000-kg van and a 2000-kg bus come closer to a circular track with a radius of 200 m.
(i) What should be the banking angle for this circular track so that automobiles traveling at 40.0 m/s can take a turn without toppling?
(ii) Should the bus move slower than the van?
The banked, circular highway curves are specifically designed for high-speed driving. To prevent vehicles from slipping outward, an 85 m radius highway curve is banked at a 28° inclination. Determine the maximum speed with which a high-speed car weighing 1800 kg can safely maneuver this curve without sliding off the road. The coefficient of friction between the tire and the road is 1.
A spacecraft is on a mission to explore Mars. When the spacecraft entered the Martian atmosphere, the commander made a balanced turn by tilting the spacecraft wings at an angle α to the horizontal. The commander maintained the center of gravity of the spacecraft in a horizontal plane. The speed Vs of the spacecraft was constant, and the spacecraft moved in a circle of radius Rs. Calculate the tilting angle α using Vs, Mars' gravitational acceleration g, and Rs. Note that the lift force is directed perpendicular to the wings and in the opposite direction of gravity.