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
Trigonometry
Newton's Laws of Motion
Formulas
Tcos(θ) = mg (Vertical Force Balance)
Tsin(θ) = mv²/r (Centripetal Force)
Lift Force = Tcos(θ) - mg
Theorems
Newton's Second Law of Motion
Trigonometric Relationships
Suitable Grade Level
Grades 10-12
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