Question

With what maximum speed a car be safely
driven along a curve of radius 40 m on a
horizontal road, if the coefficient of friction
between the car tyres and road surface is 0.3?
(g = 9.8 m/s21​

Answer 1

Given :-

Radius of curve = r = 40 m

Coefficient of Friction = µ = 0.3

Acceleration due to gravity = g = 9.8 ms-²

As we know that, when a body moves along circular or curve then its maximum velocity must be equal or greater to the product of square root of coefficient of Friction, radius of that curve and acceleration due to gravity and after crossing the maximum velocity body will skidd off the road. We can say that at maximum velocity body is on the verge of skidding.

$v \geqslant \sqrt{ \mu \: rg}$

$v \geqslant \sqrt{0.3\times40\times9.8}$

$v \geqslant \sqrt{117.6}$

$v \geqslant 10.84 m{s}^{-1}$

Hence,

The maximum velocity = v = 10.84 ms-¹