A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second
Unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the
Road surface is the same in both cases?
A) 30 m/s
B) 70 m/s
C) 40 m/s
D) 160 m/s
E) 80 m/s

Question

Quizplus · Accepted Answer

The maximum speed $v$ at which a car can round a curve without slipping is given by the formula $v = \sqrt{\mu rg}$, where $\mu$ is the coefficient of static friction, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity. Since $\mu$ and $g$ are constants, the maximum speed is directly proportional to the square root of the radius of the curve. Given that the car can travel at 20 m/s around an 80-m radius curve, for a curve with a radius four times larger (320 m), the maximum speed would be double, because the square root of 4 is 2. Therefore, the maximum speed for the 320-m radius curve is $20 m/s \times 2 = 40 m/s$.

A Car Traveling at a Steady 20 M/s Rounds an 80-M