Show that the angle of banking is independent of mass of vehicle.

Question: Show that the angle of banking is independent of mass of vehicle.

The angle of banking of a road or a track is the angle at which the surface is inclined to the horizontal to enable a vehicle to turn smoothly without skidding or slipping. It is a function of the speed of the vehicle, the radius of the turn, and the acceleration due to gravity. However, the angle of banking is independent of the mass of the vehicle.

To understand why the angle of banking is independent of the mass of the vehicle, we need to consider the forces acting on the vehicle as it goes around the turn. The main forces are the gravitational force and the centripetal force. The gravitational force depends on the mass of the vehicle, while the centripetal force depends on the speed of the vehicle, the radius of the turn, and the angle of banking.

When a vehicle goes around a banked turn, the centripetal force is provided by the horizontal component of the normal force acting on the vehicle. The angle of banking is set such that the horizontal component of the normal force provides the required centripetal force to keep the vehicle moving in a circular path without slipping or skidding. The mass of the vehicle does not affect the normal force or its horizontal component, so the angle of banking is independent of the mass of the vehicle.

In summary, the angle of banking is independent of the mass of the vehicle because the required centripetal force is provided by the horizontal component of the normal force, which is not affected by the mass of the vehicle.

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