(adsbygoogle = window.adsbygoogle || []).push({}); Model Airplane Question - centripetal acceleration and summing forces

A model airplane of mass 0.760 kg flies in a horizontal circle at the end of a 58.0 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 P6.71.

OK, ive been working on this one for 20 minutes and i have no idea. last question left on my problem set.

I found the centripetal acceleration by finding the radius of the circle in which the plane flies--since it flies on an angle on the string, i found this to be 54.40 m (NOT the 58m from the question--is this right?) my centripetal Acceleration was 22.47m/s^2

Next i summed the forces, got

SUM(Fr)=> Ac = Fsin(theta)+Tcos(theta)

SUM(Fy)=> Tsin(theta)+W=Fcos(theta)

from here i solved the 2nd equation for "F" and pluged it into the first, solved for t. I got 18.56, which is wrong. Any ideas? Im sure i missed some thing small, thanks for the help!

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# Model Airplane Question

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