Understanding the Concepts

* Centripetal Force: When an object moves in a circle, it experiences a force directed towards the center of the circle. This is called the centripetal force.

* Friction as the Centripetal Force: In this case, the force of static friction between the tires and the road provides the necessary centripetal force to keep the car moving in a circle.

* Maximum Speed: The maximum speed the car can achieve is limited by the maximum static friction force, which is proportional to the normal force (the force the road exerts on the car).

Calculations

1. Normal Force: The normal force is equal to the car's weight:

* F_normal = m * g = 1200 kg * 9.8 m/s² = 11760 N

2. Maximum Friction Force: The maximum static friction force is the product of the coefficient of static friction and the normal force:

* F_friction (max) = μ_s * F_normal = 0.45 * 11760 N = 5292 N

3. Centripetal Force: Since the friction force provides the centripetal force:

* F_c = F_friction (max) = 5292 N

4. Centripetal Force Equation: The centripetal force is given by:

* F_c = (m * v²) / r

* where:

* m = mass of the car

* v = speed of the car

* r = radius of the turn

5. Solving for Speed: Rearranging the equation to solve for 'v':

* v² = (F_c * r) / m

* v = √((F_c * r) / m)

* v = √((5292 N * 93.0 m) / 1200 kg)

* v ≈ 20.4 m/s

Answer:

The maximum speed with which the car can round the turn is approximately 20.4 m/s.