A car is negotiating a curved road of radius | vedclass

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

Question

(A) For vertical equilibrium on the road:$N \cos	heta = mg + f \sin	heta$$mg = N \cos	heta - f \sin	heta$ ... $(i)$For safe turning,the centripeta

Vedclass · Accepted Answer

$\sqrt{gR\frac{\mu_s + 	an	heta}{1 - \mu_s	an	heta}}$

Vedclass · Answer

(A) For vertical equilibrium on the road:$N \cos	heta = mg + f \sin	heta$$mg = N \cos	heta - f \sin	heta$ ... $(i)$For safe turning,the centripetal force is provided by the horizontal components of the normal force and friction:$N \sin	heta + f \cos	heta = \frac{mv^2}{R}$ ... $(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{v^2}{Rg} = \frac{N \sin	heta + f \cos	heta}{N \cos	heta - f \sin	heta}$At maximum velocity,the friction force $f$ reaches its limiting value,$f = \mu_s N$. Substituting this into the equation:$\frac{v_{\max}^2}{Rg} = \frac{N \sin	heta + \mu_s N \cos	heta}{N \cos	heta - \mu_s N \sin	heta}$Dividing the numerator and denominator by $N \cos	heta$:$\frac{v_{\max}^2}{Rg} = \frac{	an	heta + \mu_s}{1 - \mu_s 	an	heta}$Therefore,the maximum safe velocity is:$v_{\max} = \sqrt{gR \left( \frac{\mu_s + 	an	heta}{1 - \mu_s 	an	heta} ight)}$

$A$ car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

Similar Questions

$A$ coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$,the maximum angular velocity which can be given to the disc,so that the coin does not slip away,is:

On a dry road,the maximum speed of a vehicle along a circular path is $V$. When the road becomes wet,the maximum speed becomes $\frac{V}{2}$. If the coefficient of friction of the dry road is $\mu$,then the coefficient of friction of the wet road is:

$A$ cyclist on a level road takes a sharp circular turn of radius $3 \; m$ $(g = 10 \; m \cdot s^{-2})$. If the coefficient of static friction between the cycle tyres and the road is $0.2$,at which of the following speeds will the cyclist not skid while taking the turn?

Vedclass Test Series

Exam Paper Generator

Online Exam Module