A train runs along an unbanked circular track of radius of 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?
Mass of the train, m=106kg Speed of the train ,v=54km/h=54×36001000=15m/s Radius of the track, r=30m Centripetal force in this case is provided by lateral thrust of the rail. The wheel exerts an equal and opposite force on the rail from Newton's third law. This reaction force is responsible for wear and tear of the rail. The angle of banking θ tanθ=rgv2 =(30×10)(15)2 =300225 θ=tan−1(0.75)=36.87° Angle of banking=36.87°
