A race car traveling at 100 m/s enters an unbanked turn of 400 m radius. The coefficient of (static) friction between the tires and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct?
A) The race car will crash into the outer wall.
B) The race car will crash into the inner wall.
C) The car will stay in the center of the track.
D) The car will stay in the center of the track if the driver speeds up.
E) The car would stay in the center of the track if the radius were reduced to 200 m.

Question

Quizplus · Accepted Answer

The centrifugal force acting on the car is given by Fc = mv^2/r, where m is the mass of the car, v is its velocity, and r is the radius of the turn. The maximum static frictional force that the track can exert on the car is given by Ff = μN, where μ is the coefficient of friction and N is the normal force on the car. In an unbanked turn, the normal force is simply the weight of the car (N = mg). Thus, the maximum speed that the car can safely travel around the turn is given by √(μgr), where g is the acceleration due to gravity.

Plugging in the given values, we get √(1.1 x 9.8 x 400) = 66.6 m/s. Since the car is traveling faster than this speed, it will not be able to make the turn and will crash into the outer wall.

A Race Car Traveling at 100 M/s Enters an Unbanked