A train runs along an unbaked circular bend of radius 30 m at a speed

1.	A train runs along an unbaked circular bend of radius 30 m at a speed of 54 kmh-1. 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?
Answer» (i) The centripetal force is provided by the lateral force acting due to rails on the wheels of the train. (ii) The outer rails wear out faster (iii) tanθ = v²/rg ⇒ tanθ = {(15)²}/{30 x 9.8} = 0.7653 = tan 37.4° θ = 37.4° = 37° 25'

A train runs along an unbaked circular bend of radius 30 m at a speed of 54 kmh-1. 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?

Answer»

(i) The centripetal force is provided by the lateral force acting due to rails on the wheels of the train.

(ii) The outer rails wear out faster

(iii) tanθ = v²/rg ⇒ tanθ = {(15)²}/{30 x 9.8} = 0.7653 = tan 37.4°

θ = 37.4° = 37° 25'