Question

A car has a steady speed of 25m/s along a horizontal curve of radius 115m. What is the minimum coefficient of static friction between the road and the car’s tires that will allow the car to travel at this speed without sliding?

Answer 1

$\text{ according to 2 Newton's law:}$

$\vec F = m*\vec a$

$\vec a = \frac{v^2}{r}$

$\vec F = m*\frac{\vec{ v^2}}{r}$

$\text{also: }$

$\vec F = m*\vec{g}+\vec N +\vec{F_{fr}}$

$\text{Horizontal force projections:}$

$F= F_{fr}(1)$

$\text{Vertical force projections:}$

$N-mg=0$

$N= mg$

$F_{fr} =\mu N=\mu mg$

$\text{From equality(1):}$

$m*\frac{\vec{ v^2}}{r} = \mu mg$

$\mu = \frac{v^2}{r*g}= \frac{25^2}{115*9.8}=0.55$

$\text{Answer : }\mu =0.55$