A metre gauge train is moving at 72 kmph along a curved railway track of radius of curvature 500 m. Find the elevation of the outer rail above the inner rail so that there is no side thrust on the outer rail.
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A metre gauge train is moving at 72 kmph along a curved railway track of radius of curvature 500 m. Find the elevation of the outer rail above the inner rail so that there is no side thrust on the outer rail.
A metre gauge train is moving at 72 kmph along a curved railway track of radius of curvature 500 m. Find the elevation of the outer rail above the inner rail so that there is no side thrust on the outer rail.
Data : r = 500 m, v = 72 kmph = 72 × \(\frac{5}{18}\) m/s
= 20 m/s, g = 10 m/s2 , l = 1 m
tan θ = \(\frac{v^2}{rg}\)
= \(\frac{(20)^2}{500\times 10}\) = 0.08
The required angle of banking,
θ = tan-1 (0.08) = 4°4′
θ = tan-1 (0.08) = 4°4′
The elevation of the outer rail relative to the inner rail,
h = l sin θ
= (1)(sin 4°4′) = 0.0709 m = 7.09 cm