A model airplane of mass 0.750 kg is flying at a constant speed of 6.0 m/s in a

Question

A model airplane of mass 0.750 kg is flying at a constant speed of 6.0 m/s in a level, horizontal circle of radius 1.20 m at a height of 1.60 m. The plane is tethered to the ground by a cord that makes an angle of 36.87 degree from the vertical. The airplane's wings are horizontal so the air pushes vertically upward on the wings. The free body diagram is shown at right for a particular moment in time. Write the sum of the forces equations for the airplane. (NOTE: Use the coordinate system provided!) What is the magnitude of the tension, T, in the cord? What is the magnitude of the upward lifting force, F_Lift, on the plane's wings?

Explanation / Answer

All forces

1. liftind force Fl

2. gravitational force Fg

3. Tension of string Ft

4. Centrifugal force Fc

So the forces balance in the vertical direction

Fl = Ft cos(36.87 degrees) + Fg ------(1)

Horizontal force

Fc = Ft sin(36.87 degrees) ------(2)

Part B:

Tension T = Ft

Fc = mv2/r =0.75*6*6/1.2 = 22.5N

from using the equation (2)

T = Ft = 22.5/sin(36.87 degrees) = 22.5*5/3 = 37.5N

Part C

lifting force

Fl = mg + 22.5*4/5 = 90+7.5 = 97.7N

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