A model airplane of mass 0.770 kg flies in a horizontal circle at the end of a 5

Question

A model airplane of mass 0.770 kg flies in a horizontal circle at the end of a 56.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0 with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic lift, which acts at 20.0 inward from the vertical as shown in Figure P6.61.

A model airplane of mass 0.770 kg flies in a horizontal circle at the end of a 56.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0½ with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic lift, which acts at 20.0½ inward from the vertical as shown in Figure P6.61.

Explanation / Answer

my dear here is your desired solution
R=56.cos20 m.= 52.622m
The total horizontal force acting on the plane is
F = mv^2/R = 0.770 x 35 x 35/ 52.622 = 17.925N

The aerodynamic lift on the plane has a radially inward (horizontal) acting component A = m.g.sin20 = 0.770 x 9.81 sin20 = 2.583N
which provides part of the above force F.
The horizontal force required from the wire is therefore F - A

and therefore the tension in the wire (F - A) /cos20 = 16.3212 N

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