Question

A train rounds an unbanked circular bend of radius 30 m and speed 54km/hr mass of train is 106 what is the angle banking to prevent wearing of rail ?

Answer 1

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(1) The centripetal force is provided by the lateral force acting due to rails on the wheels of the train.

(2) Outer rails

$(3) \: \: \: \: \tan0 = \frac{ {v}^{2} }{rg} = \frac{ {(15)}^{2} }{30 \times 9.8} \\ \tan 0 \ = 0.7653 \\ \\ 0 = {37.4}^{0}$

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Answer 2

the centripetal force required by the train to cross the circular bend is provided by the lateral thrust exerted by the outer rails on the wheels .

According to Newton's law train also exert equal and opposite direction force on the rails causing it wear and tear .

speed of train = 54 km/h

= 54 *5/18 m/s

= 15 m/s

radius of ciruclar bend = 30 m

mass of train = 10^6 kg

Let train inclined {theta} angle with vertical shown in figure .

in equilibrium ,

vertical components :

Ncos {theta} = mg -----------(1)

Nsin {theta} = mv^2/r ---------(2)

divide (2) and (1)

tan {theta} = v^2/rg

= (15)^2/(30)(10)

= 3/4

tan {theta} = 3/4

{theta} = tan^-1 {3/4}