A train rounds an unbanked circular bend of radius 30 m at a speed of `54 km//h` The mass of the train is `10^(6)` kg What provides the centripetal force required for this purpose ? The engine or the rails ? What is the angle of banking required to prevent out the rails ?

Explanation

The centripetal force is provided by the lateral thrust exerted by the rails on the wheels By Newton s 3 rd law , the train exerts an equal and opposite thrust on the rails causing its wear and tear . Obviously the outer rail will wear out faster due to the larger force exerted by the train on it .
Here ` upsilon = 54 km//h = (54 xx 1000)/(60 xx 60 ) = 15 m//s `
` g = 9.8 m s^(-2) `
As ` tan theta = upsilon^(2)/(r g ) = (15 xx 15 )/(30 xx 9.8 ) = 0.76 :. theta = tan^(-1) 0.76 = 37.4^(@)` .