A race car travelling at 100 m/s during a race at Bathurst enters an unbanked turn of 400 m radius. The coefficient of (static) friction between the tyres 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 centre of the track.
D)The car will stay in the centre of the track if the driver speeds up.
E)The car would stay in the centre of the track if the radius were reduced to 200 m.

Question

Quizplus · Accepted Answer

In an unbanked turn, the centrifugal force acting on the car is provided only by the frictional force between the tires and the track. The maximum frictional force that can act on the tires is given by:
frictional force = coefficient of friction x normal force
The normal force is the force with which the track pushes up on the car and is equal to the weight of the car. The maximum frictional force is therefore limited by the weight of the car and the coefficient of friction. In this case, the maximum frictional force is:
frictional force = (1.1) x (mass of car) x (acceleration due to gravity)
= (1.1) x (mass of car) x (9.8 m/s^2)
In order for the car to remain in the turn, the centrifugal force acting on the car (mv^2/r) must be less than or equal to the maximum frictional force. Solving for the maximum speed the car can go around the turn without sliding:
mv^2/r <= (1.1) x (mass of car) x (9.8 m/s^2)
v^2 <= (1.1) x (9.8 m/s^2) x (400 m)
v <= 83.4 m/s
Since the car is travelling at 100 m/s, it will not be able to make the turn and will slide outwards, crashing into the outer wall.

A Race Car Travelling at 100 M/s During a Race