Math Problem Statement
A model airplane of mass 0.700 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 62.0-m-long control wire as shown in Figure (a). The forces exerted on the airplane are shown in Figure (b): the tension in the control wire, the gravitational force, and aerodynamic lift that acts at 𝜃 = 20.0° inward from the vertical. Compute the radius, lift, and tension in the wire, assuming it makes a constant angle of 𝜃 = 20.0° with the horizontal. Use g=9.8 m/s2. radius
Solution
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Math Problem Analysis
Mathematical Concepts
Circular Motion
Forces
Trigonometry
Newton's Second Law
Formulas
Centripetal Force: F = m * v² / r
Gravitational Force: F = m * g
Lift Force (vertical and horizontal components): F_lift = m * g / cos(θ)
Tension in the wire: T = sqrt(T_x² + T_y²)
Theorems
Newton's Second Law
Equilibrium of Forces in Circular Motion
Suitable Grade Level
Grades 11-12 (Physics)
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