To find the minimum speed the car can navigate the curve without relying on friction, we can use the concept of centripetal force. The centripetal force required to keep the car moving in a circle of radius r with a mass m and velocity v is given by:

F = (mv^2)/r

In this case, the centripetal force is provided by the horizontal component of the normal force (Nsinθ). The vertical component of the normal force (Ncosθ) balances the weight of the car (mg).

Nsinθ = mv^2/r

Since we want to find the minimum speed, we can assume the car is just about to slip or start sliding up the incline. At this point, the frictional force is zero. Therefore, the force of friction (μN) is zero, where μ represents the coefficient of static friction.

Now, we can balance the vertical forces to find the normal force (N):
Ncosθ = mg

N = mg/cosθ

Substituting this into the equation for the centripetal force:

(mg/cosθ)sinθ = mv^2/r

We can simplify this equation to:
g tanθ = v^2/r

Now, we can solve for the minimum speed v:

v = sqrt(rg tanθ)

Given:
Radius (r) = 150 meters
Banking angle (θ) = 20 degrees

Plugging in these values:

v = sqrt(9.8 x 150 x tan(20))
≈ sqrt(1455.59)
≈ 38.13 m/s

Therefore, the minimum speed the car can navigate the curve without relying on friction is approximately 38.13 m/s.

To find the tension in the car's tires due to centripetal force, we can use the formula:
T = (mv^2)/r

Substituting the known values:
T = (m x (38.13)^2) / 150

Without knowing the mass of the car, we cannot determine the exact value of the tension in the car's tires.

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