A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 106 kg. What provides the centripetal force required for this purpose — The engine or the rails ? What is the angle of banking required to prevent wearing out of the rail ?
Given that the radius of the circular track on which the train runs is 30 m , the speed of the train is 54 km / h and the mass of the train is 10 6 kg .
The equation of the centripetal force is,
F = m v 2 r
Here, the mass of the train is m , the velocity of the train is v and the radius of the circular track is r.
The centripetal force that is applied for negotiating the circular track is provided by the force of friction due to the rails that are rubbing on the wheels of the train. The angle of banking is provided to prevent the wearing of the rails by the wheels of the train.
The equation to determine the angle of banking of the train is,
tan θ = v 2 r g
Substitute the values in the above equation.
tan θ = ( ( 50 km / hr ) × ( 5 18 m / s 1 km / hr ) ) 2 ( 30 ) ( 10 ) θ = tan − 1 ( 15 × 15 30 × 10 ) = 37 °
Thus, the angle of the banking is 37 ° .
Given that the radius of the circular track on which the train runs is
The equation of the centripetal force is,
Here, the mass of the train is
The centripetal force that is applied for negotiating the circular track is provided by the force of friction due to the rails that are rubbing on the wheels of the train. The angle of banking is provided to prevent the wearing of the rails by the wheels of the train.
The equation to determine the angle of banking of the train is,
Substitute the values in the above equation.
Thus, the angle of the banking is
