An aerobatic airplane flying at a constant 90.0 m/s makes a horizontal turn of radius 245 m. The pilot has a mass of 80.0 kg. What is the bank angle of the airplane?

Question

25-12-2024
Physics

College

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An aerobatic airplane flying at a constant 90.0 m/s makes a horizontal turn of radius 245 m. The pilot has a mass of 80.0 kg. What is the bank angle of the airplane?

Answer :

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ssprabhatsingh24 ssprabhatsingh24 · Answer 1 · 2025-02-20T16:52:57-05:00

Final answer:

The bank angle of an airplane making a horizontal turn can be calculated by considering the centripetal force and lift force. The horizontal component of the lift force provides the centripetal force and the vertical component balances the airplane's weight. By substituting the given values into these equations, we can solve for the bank angle.

Explanation:

The question asks for the bank angle of an aerobatic airplane making a horizontal turn. This is actually a physics problem which we can solve by considering centripetal force and lift force. The centripetal force required to keep the airplane in a circular path is provided by the lift force, which acts at right angles to the wing. In level flight, the lift force equals the airplane's weight, but in banked turn, it's greater than the weight.

The horizontal component of the lift force provides the centripetal force and the vertical component balances the airplane's weight. So, we have two equations: Lift Force sin θ = Weight, and Lift Force cos θ = mv²/r. In these equations, m is the mass of the pilot, v is the speed of the airplane, and r is the radius of the turn. Substituting the given values and solving for θ gives the bank angle.

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