The two rails of a railway track are 1.7 m apart. At a circular curve of radius 1.5 km, a train should have an optimum speed of 108 kmph so that there is no side thrust on the outer rail. Find the angle of banking of the track and the elevation of the outer rail above the inner rail .

Explanation

Data : l = 1.7 m , r = 1.5 k m ,=1500 m ,, v = 108 kmph.
`(108 xx 10^(3)m)/(3600 s) = 30 m//s ,g =9.8 m//s^(2)`
(i) If `theta` is the banking angle.
` tan theta =(v^2)/(rg) = (30^(2))/(1500 xx 9.8) = 6/68 =0.06122`
` theta = tan^(-1) 0.6122 = 3^(@) 30`
(ii) The elevation of the outer rail above the inner rail.
`h = l sin theta= 1.7 xx sin (3^(@) 30)`
= `1.7 xx 0.06111 = 0.1038 m or 10.38 cm `