Question

What is meant by banking of roads? Obtain an expression for the maximum speed wch a vecle can safely negotiate a curved road banked at an angle θ .

Answer 1

banking of roads : the phenomenon of raising outer edge of the curved road above the inner edge is to take a safer turn is called Banking of Roads.

Let a car of mass m moves with speed v m/s in a curved road banked at an angle $\theta$. and also given that roughness of curved surface is $\mu_s$.

see diagram,

$\Sigma F_x=\frac{mv^2}{r}=Nsin\theta+\mu_sNcos\theta$.......(1)

$\Sigma F_y=Ncos\theta-\mu_sNsin\theta-mg$........(2)

from equations (1) and (2),

$\boxed{\bf{v_{max}=\sqrt{\frac{rg(sin\theta+\mu_s cos\theta)}{(cos\theta-\mu_s sin\theta)}}}}$

case 1 :- when curved surface is frictionless.e.g., $\mu_s=0$

then, $v_{max}=\sqrt{rgtan\theta}$

case 2 :- for flat roadway. e.g., $\theta=0^{\circ}$

then, $v_{max}=\sqrt{\mu_s rg}$

Answer 2

Answer:

1. the phenomenon of raising the outer edge of the curved load above the inner edge is to safer turn is called the banking of road .

Explanation:

fr=nv^2/r= nsin+usNcos..1

fy=

ncos-usNsin-mg...2

vmax=√rg(sin+usNcos)/cos-usSino