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

r = 30 m, v = 54 km `h^(-1) = (54xx5)/(18) ms^(-1)`
= 15 `ms^(-1) " " m = 10^(6)` kg. `" " theta` = ?
(i) The centripetal force is provided by the lateral thrust by the outer rail on the flanges of the wheel of the train. The train causes an equal and opposite thrust on the outer rail (Newton’s third law of motion).
Thus, the outer rails wears out faster.
(ii) tan `theta = (v^(2))/(rg) = (15 xx 15)/(60 xx 9.8) = 0.7653`
`therefore " "theta = tan^(-1) (0.7653) = 37.43^(@)`