An 855-kg race car can drive around an unbanked turn at a maximum speed of 61 m/s without slipping. The turn has a radius of curvature of 165 m. Air flowing over the car's wing exerts a downward-pointing force (called the downforce) of 10900 N on the car.

(a) What is the coefficient of static friction between the track and the car's tires?

(b) What would be the maximum speed if no downforce acted on the car?
m/s

To find the coefficient of static friction between the track and the car's tires, we need to consider the forces acting on the car as it goes around the turn. The only horizontal force acting on the car is the force of friction between the tires and the track.

(a) Let's start by calculating the centripetal force required for the car to negotiate the turn without slipping. The centripetal force is given by:

F_c = m * v^2 / r

where F_c is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of curvature.

Plugging in the values, we have:

F_c = (855 kg) * (61 m/s)^2 / 165 m

F_c ≈ 17486.03 N

This is the minimum force of static friction needed to keep the car from slipping. Therefore, the force of static friction between the tires and the track should be equal to this value.

Now, let's calculate the force of static friction using the formula:

F_f = μ * N

where F_f is the force of friction, μ is the coefficient of static friction, and N is the normal force between the car and the track. In this case, the normal force is equal to the weight of the car.

The weight of the car is given by:

F_weight = m * g

where g is the acceleration due to gravity.

Plugging in the values, we have:

F_weight = (855 kg) * (9.8 m/s^2)

F_weight ≈ 8380.1 N

Now, equating the force of static friction to the centripetal force, we get:

F_f = F_c

μ * F_weight = F_c

μ = F_c / F_weight

μ ≈ 17486.03 N / 8380.1 N

μ ≈ 2.084

Therefore, the coefficient of static friction between the track and the car's tires is approximately 2.084.

(b) To find the maximum speed if no downforce acted on the car, we need to consider the forces acting on the car in this scenario. With no downforce, the normal force between the car and the track will be reduced, resulting in a decrease in the maximum possible force of static friction.

The new normal force is given by:

N_new = N - F_downforce

where N_new is the new normal force, N is the original normal force (weight of the car), and F_downforce is the downforce exerted by the air on the car's wing.

Plugging in the values, we have:

N_new = 8380.1 N - 10900 N

N_new ≈ -2520.9 N

Since the normal force cannot be negative, this means that the maximum speed without any downforce acting on the car is zero. In other words, the car would not be able to negotiate the turn without any downforce.

Therefore, the maximum speed if no downforce acted on the car would be zero m/s.