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Question -

A train runs along an unbanked circulartrack 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 orthe rails? What is the angle of banking required to prevent wearing out of therail?



Answer -

Radius of the circular track, r =30 m

Speed of the train, v = 54km/h = 15 m/s

Mass of the train, m = 106 kg

Thecentripetal 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 oppositeforce on the rail. This reaction force is responsible for the wear and rear ofthe rail

The angle of banking θ, isrelated to the radius (r) and speed (v) by the relation:


Therefore,the angle of banking is about 36.87°.

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