Question

Suppose the coefficient of static friction between the road and the tires on a car is 0.683 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 26.9 m radius?

Answer 1

Answer:

v=13.4 m/s

Explanation:

The centripetal acceleration the car experiments is due to friction, so what we need is to write our equation using the maximum static friction, which is the case on the verge of sliding:

$ma_{cp}=f=\mu_s N$

Which means (since we are in a horizontal surface):

$m\frac{v^2}{R}=\mu_s mg$

So the maximum speed before sliding is:

$v=\sqrt{\mu_s Rg}$

Which for our values is:

$v=\sqrt{(0.683)(26.9m)(9.81m/s^2)}=13.4m/s$