On a snowy day, when the coefficient of friction μs between a car’s tires and the road is 0.50, the maximum speed that the car can go around a curve is 20 mph. what is the maximum speed at which the car can take the same curve on a sunny day when μs=1.0?

28.1 mph

Explanation:

The force of friction acting on the car provides the centripetal force that keeps the car in circular motion around the curve, so we can write:

(1)

where

is the coefficient of friction

m is the mass of the car

g = 9.8 m/s^2 is the acceleration due to gravity

v is the maximum speed of the car

r is the radius of the trajectory

On the snowy day,

So the radius of the curve is

Now we can use this value and re-arrange again the eq. (1) to find the maximum speed of the car on a sunny day, when . We find: