Final answer:
The banking angle for a car of mass 2.3 Mg (Megagrams) traveling at 69 km/hr around a curve with a radius of 60 m, where friction is not relied upon, is approximately 30.5 degrees.
Step-by-step explanation:
The student is asking about the angle at which a curve should be banked for a car traveling with a certain uniform speed without relying on friction. To solve for the banking angle θ, we can use the following physics principles and equations that relate the force components on a car moving on a banked curve and gravity:
Fc = mv2/r
tan(θ) = v2/(rg)
where Fc is the centripetal force needed to keep the car on the curve, m is the mass of the car, v is the velocity of the car, r is the radius of the curve, g is the acceleration due to gravity, and θ is the banking angle of the curve.
First, convert the mass 2.3 Mg to kilograms (2,300 kg) and the velocity to meters per second (69 km/h to 19.17 m/s). Next, solve the second equation for θ:
tan(θ) = (19.17 m/s)2 / (60 m × 9.8 m/s2)
Calculate tan(θ) and then find θ by taking the arctan (inverse tangent) of that result. When calculating, you get:
tan(θ) ≈ 0.5905
θ ≈ arctan(0.5905) ≈ 30.5 degrees
So, the banking angle is approximately 30.5 degrees.