Final answer:
During a 45-degree banked turn, an airplane weighing 4500 pounds would require approximately 6366 pounds of lift force to maintain altitude, due to the increased lift needed to provide for both the vertical and horizontal components.
Step-by-step explanation:
To calculate the weight the airplane structure would be required to support during a 45 degree banked turn while maintaining altitude, we can use principles from physics related to circular motion and banking angles. The lift force has two components during a banked turn: a vertical component that must counteract the weight of the airplane and a horizontal component that provides the centripetal force necessary for the turn. At a 45-degree banking angle, the lift force required is greater than the weight of the aircraft to provide the necessary vertical and horizontal components.
Using the formula for lift force in a banked turn, L = W / cos(θ), where L is the lift, W is the weight, and θ is the banking angle, we find that:
L = 4500 pounds / cos(45 degrees)
L = 4500 pounds / 0.7071
L ≈ 6366 pounds
Therefore, the airplane structure during a 45-degree banked turn would approximately need to support 6366 pounds to maintain altitude.