A model airplane of mass 0.780 kg flies with a speed of 35.0 m/s in a horizontal

Question

A model airplane of mass 0.780 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 a lift that acts at theta = 20.0 degree inward from the vertical. Compute the radius, lift, and tension in the wire assuming it makes a constant angle of theta = 20.0 degree with the horizontal. radius m lift ______ N tension Your response differs from the correct answer by more than 10%. Double check your calculations. N

Explanation / Answer

Given

mass of airplane m = 0.780 kg, speed v = 35 m/s
lenght of the wire l = 62 m

the angle theta with verical is = 20 degrees

here the force mg = F_lift cos theta ==> F_lift = mg/cos theta

                   F_lift = 0.780*9.8/cos20 = 8.135 N

here the forces acting on the airplane are

       Fc = TX+ Flift_x

       mv^2/r cos 20 = Tx + F_lift* sin theta

       0.780*35^2/59 cos20 -8.135sin20 = Tx
  

       Tx = 12.44 N

and

       mg cos theta -mg -Ty = 0 ==> Ty = mg(cos theta -1) = 0.78*9.8(cos20-1)

       Ty = -0.461 N

the magnitude is T = sqrt((12.44)^2+(-0.461)^2) = 12.5 N

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