Question

A train has to negotiate a curve of radius $400$m. By how much height should the outer rail be raised with respect to inner rail for a speed of $48$ km/hr? The distance between the rails is $1$m.

Answer 1

radius of curved path is $r$. width of path is$b$$m$. the outer edge is raised by $h$ $w.$ $r$ . $t$ inner edge so that a car with speed $v$ can pass safe over it. the value of his

$tan\theta =\frac{v²}{rg}$

$=\frac{h}{bh}=\frac{v²b}{rg}$

substituting the values according to given question,

$v=\frac{48km}{h}=\frac{(48\ast 1000)}{60\ast 60m{s}^{-1}}=\frac{40}{3}m{s}^{-1}$

$b=1m$

$r=400m$

$g=9.8m{s}^{-1}2$

$h=\left(\frac{40}{3}\right)²\ast \frac{1}{400}\ast 9.8$

$=0.0045m$

$=4.54cm$