A railway line is taken round a circular arc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $m$ be the mass of the train,$R = 1000 \ m$ be the radius of the curve,and $	heta$ be the angle of banking.In the frame of the train,the forc

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let $m$ be the mass of the train,$R = 1000 \ m$ be the radius of the curve,and $	heta$ be the angle of banking.In the frame of the train,the forces acting along the inclined plane are the component of gravity $mg \sin 	heta$,the centrifugal force $\frac{mv^2}{R} \cos 	heta$,and the lateral force $F$ exerted by the rails.For speed $v_1 = 10 \ ms^{-1}$,the train tends to slide down,so the lateral force $F_1$ on the inner rail is given by:$F_1 + \frac{mv_1^2}{R} \cos 	heta = mg \sin 	heta$For speed $v_2 = 20 \ ms^{-1}$,the train tends to slide up,so the lateral force $F_2$ on the outer rail is given by:$\frac{mv_2^2}{R} \cos 	heta = mg \sin 	heta + F_2$Given $F_1 = F_2 = F$,we equate the expressions:$mg \sin 	heta - \frac{mv_1^2}{R} \cos 	heta = \frac{mv_2^2}{R} \cos 	heta - mg \sin 	heta$$2mg \sin 	heta = \frac{m}{R} \cos 	heta (v_1^2 + v_2^2)$$2g 	an 	heta = \frac{v_1^2 + v_2^2}{R}$$	an 	heta = \frac{10^2 + 20^2}{2 	imes g 	imes 1000} = \frac{100 + 400}{2000g} = \frac{500}{2000g} = \frac{1}{4g}$Therefore,$4g 	an 	heta = 4g 	imes \frac{1}{4g} = 1$.

Similar Questions

If $\left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \ldots\left(1+\frac{2n+1}{n^2}\right)=121$,then $n=$

Into how many kingdoms is the domain $Eukarya$ divided?

The $Ca^{2+}$ and $F^{-}$ ions are located in a $CaF_2$ crystal,respectively at face-centered cubic lattice points and in:

The energy of the electron at infinite distance from the nucleus in Bohr's Model is taken as

Vedclass Test Series

Exam Paper Generator

Online Exam Module