Question

You are exiting a highway and need to slow down on the off-ramp in order to make the curve. It is rainy and the coefficient of static friction between your tires and the road is only 0.4. If the radius of the off-ramp curve is 36 m, then to what speed do you need to slow down the car in order to make the curve without sliding?

Answer 1

Answer:

11.87m/s

Explanation:

To solve this problem it is necessary to apply the concepts related to frictional force and centripetal force.

The frictional force of an object is given by the equation

$F_r = \mu N$

Where,

$\mu =$Friction Coefficient

N = Normal Force, given also as mass for acceleration gravity

In the other hand we have that centripetal force is given by,

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

The force experienced to stay on the road through friction is equal to that of the centripetal force, therefore

$F_r = F_c$

$\mu mg = \frac{mv^2}{R}$

Re-arrange to find the velocity,

$V = \sqrt{R\mu g}$

$V = \sqrt{36*0.4*9.8}$

$V = 11.87m/s$

Therefore the speed that it is necessaty to slow down the car in order to make the curve without sliding is 11.87m/s