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 `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 prevnt wearing out of the rail ?

Explanation

The centripetal force is provided by the lateral thrust exerted by the rails on the wheels . By Newton's 3rd 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 froce exerted by the train on it .
Here , `v=54km//h=(54xx1000)/(60xx60)=15m//s.,`
`g=9.8ms^(-2)`
As `tantheta=(v^(2))/(r" "g)=(15xx15)/(30xx9.8)=0.76,`
`thereforetheta=tan^(-1)0.76=37.4^(@)`