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?

Question

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?

Philoid · Accepted Answer

Given:

Radius of track, R = 30 m

Speed of train, v = 54 Km/h = 15ms

Mass of the train, m = 10⁶ Kg

The centripetal force is provided by the lateral thrust of the rail on the wheel. As per Newton’s third law of motion, the wheel exerts an equal and opposite force on the rail. This reaction force is responsible for the wear and tear of the rail.

The angle of banking Θ, is related to the radius (R) and speed (v) by the relation:

R = v²/ (g tan Θ) …(1)

→ tanΘ = 0.75

→ Θ = 36.87°

The angle of banking is about 37°.

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?

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?