Question

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?

Answer 1

To solve this problem it is necessary to take into account the concepts related to Centripetal Force and Friction Force.

In the case of the centripetal force, we know that it is defined as

$F_c = \frac{mv^2}{R}$

Where,

m=mass

v= velocity

r= Radius

In the case of the Force of Friction we have to,

$F_f = \mu m*g$

Where,

$\mu =$Friction Constant

m= mass

g= gravity

According to the information given, the centripetal force must be less than or equal to the friction force to stay on the road, in this way

$\frac{mv^2}{R} \leq \mu m*g$

Re-arrange to find the velocity,

$v \leq \sqrt{\mu gR}$

$v \leq \sqrt{(0.6)(9.8)(300)}$

$v \leq 42m/s$

Therefore la velocidad del carro debe ser igual o menor a 42m/s para mantenerse en el camino