Question

Question 5.31 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 106 kg. What provides the centripetal force required for this purpose – The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

Chapter Laws Of Motion Page 112

Answer 1

Hi__
hope u know
angle of bank formulas
it is
tanQ=(velocity)^2/ radius x acceleration

use this we get
Q=36.87 degree
hope it help

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}