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)160 m/s
B)80 m/s
C)70 m/s
D)40 m/s
E)30 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 for both curves, the maximum speed is directly proportional to the square root of the radius. 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, making it 40 m/s.

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