How Do You Calculate Tension in a Wire When a Model Airplane Flies in a Circle?

[integra2k20]

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, I've 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? I am sure i missed some thing small, thanks for the help!

 

[rsk]

Fc = Tcos20 + Flsin20

mg = -Tsin20 + Flcos20 with Fl = life, surely?

I don't think you have to solve for Fl, just calculate Fc then get Fl in terms of T and just solve for T.

Do you know what the answer should be?

Sorry - edited after looking more closely at picture...

 

[integra2k20]

Fc = Tcos20 + Flsin20

mg = -Tsin20 + Flcos20 with Fl = life, surely?

I don't think you have to solve for Fl, just calculate Fc then get Fl in terms of T and just solve for T.

Do you know what the answer should be?

Sorry - edited after looking more closely at picture...

that is effectively what i did. i got Fl in terms of T and plugged it in, had the same equations you did. no, don't know what the answer should be, it is an online webassign assignment which you get 5 chances to get the right answer. i have 3 wrong so far

 

[integra2k20]

Fc = Tcos20 + Flsin20

mg = -Tsin20 + Flcos20 with Fl = life, surely?

I don't think you have to solve for Fl, just calculate Fc then get Fl in terms of T and just solve for T.

Do you know what the answer should be?

Sorry - edited after looking more closely at picture...

is Fc the same as centripetal acceleration? v^2/r?

 

[andrevdh]

You wrote:

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

while you probably ment

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

where

$$F_C = \frac{mv^2}{r}$$

I did follow the same procedure as you but got a different answer.
Best you show all the steps so that we can comment on your work.

What is very interesting about my final formula - just before calculating the tension in the string - is that this formula suggest that if the airplane flew in a circle inclined at $$20^o$$ to the horizontal (in the plane of the direction of the sting, that is if the hobbyist stood on a platform and let it fly in a plane inclined at twenty degrees w.r.t. the horizontal in stead of a horizontal plane as in the problem) with the same speed the tension (when the airplane is at the top of this inclined plane- at point B) would be exactly the same as the case is with the stated problem you are trying to solve.