An airplane flies at 120.0 m / s and banks at a 30^∘ angle. If its mass is 2.50 ×10^3 kg, (a) wh

step 1 Well, we have mass M that is equal to 2 .5 times 10 to the power 3 kilogram. And we have theta.

An airplane flies at 120.0 m / s and banks at a 30^∘ angle....

An airplane flies at $120.0 \mathrm{m} / \mathrm{s}$ and banks at a $30^{\circ}$ angle. If its mass is $2.50 \times 10^{3} \mathrm{kg},$ (a) what is the magnitude of the lift force? (b) what is the radius of the turn?

Key Concepts

Aerodynamic Lift

Aerodynamic lift is the force generated by an aircraft’s wings that acts perpendicular to the relative airflow. This force is crucial for flight as it counteracts gravity, enabling an airplane to maintain altitude, and, when the airplane is banked, provides both a vertical component to balance gravity and a horizontal component to produce the necessary centripetal force for turning.

Banked Turn

A banked turn occurs when an airplane tilts its wings to one side, causing the lift force to be angled away from purely vertical. This tilting means that the lift force has a horizontal component, which acts as the centripetal force required for circular motion during a turn, while the vertical component continues to oppose the gravitational force, maintaining altitude.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. In the context of a banked turn, the horizontal component of the lift force supplies this centripetal force. Its magnitude determines how sharply an airplane can turn at a given speed, linking the dynamics of circular motion to the forces generated by the aircraft's wing design and speed.

Force Decomposition

Force decomposition involves breaking a force into its components along chosen axes. In a banked turn, the lift force is decomposed into vertical and horizontal components. The vertical component must balance the gravitational force to maintain level flight, while the horizontal component provides the centripetal force necessary to execute the turn, showcasing the practical application of vector resolution in physics.

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