A car enters a level, unbanked semi-circular hairpin turn of 100 m radius at a speed of 28 m/s. The coefficient of friction between the tires and the road is μ = 0.800. If the car maintains a constant speed of 28 m/s, it will
A) attempt to dig into the road surface.
B) tend to veer toward the center of the semicircle.
C) arrive safely at the end of the semicircle.
D) tend to veer toward the outside of the circle.
E) veer toward the center for the first quarter-circle, then veer toward the outside for the second quarter-circle.

Question

Quizplus · Accepted Answer

The car will arrive safely at the end of the semicircle if the centripetal force acting on the car is less than or equal to the maximum frictional force that the tires can provide.

Centripetal force = (mass of car) x (centripetal acceleration) 
Centripetal acceleration = (velocity)^2 / (radius) 
Max frictional force = (coefficient of friction) x (normal force)

Assuming a flat road surface and level turn, the normal force is equal to the weight of the car. 
Max frictional force = (0.8) x (weight of car)

Now, we can compare the centripetal force and the max frictional force: 
Centripetal force = (mass of car) x (centripetal acceleration) 
Centripetal force = (mass of car) x [(velocity)^2 / (radius)] 
Centripetal force = (mass of car) x (28 m/s)^2 / (100 m) 
Centripetal force = (mass of car) x 7.84 m/s^2

Now let's compare the centripetal force and the max frictional force: 
Centripetal force <= max frictional force 
(mass of car) x 7.84 m/s^2 <= (0.8) x (weight of car)

We can simplify this to: 
mass of car <= 0.102 x weight of car

Since the mass of the car is a fixed value, the weight of the car cannot exceed a certain limit in order for the car to make the turn safely. Based on the given information, we cannot determine the weight of the car or whether it falls under this limit. However, we can say with certainty that the car will arrive safely at the end of the semicircle as long as the weight of the car is within the safe limit.

A Car Enters a Level, Unbanked Semi-Circular Hairpin Turn of 100