Final answer:
The minimum turning radius of a 1700-kg car traveling at 20 m/s, with a maximum frictional force of 12,000 N between its tires and the road, is 56.67 meters.
Step-by-step explanation:
To find the minimum turning radius of the car, we need to use the centripetal force equation. The centripetal force required for a car to turn in a circular path is provided by the frictional force between the tires and the road. The centripetal force (Fc) is given by the formula Fc = (mv2)/r, where m is the mass of the car, v is the velocity, and r is the radius of the turn.
The maximum frictional force that can act without the car slipping is given as 12,000 N. Using the values provided:
Fc = (mv2)/r
Fc = (1700 kg * (20 m/s)2)/r
Fc = 680,000/r
Since Fc must be less than or equal to the maximum frictional force,
680,000/r <= 12,000
So the minimum radius r for which this inequality holds true is:
r >= 680,000 / 12,000
r >= 56.67 meters
Therefore, the minimum turning radius of the car is 56.67 meters.