Model Airplane: Tension/Circular Motion/Lift

[phy221]

Homework Statement

A model airplane of mass 0.710 kg flies in a horizontal circle at the end of a 63.0 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 the figure.

Homework Equations

Fnet = ma

a(radial) = v^2/r

The Attempt at a Solution

m = .710kg
v(horizontal) = 35m/s
mg = 6.958N
r = 63cos20 = 59.20m
a(radial) = (35^2)/59.20 = 20.69m/s^2
F(radial) = .710(20.69) = 14.6899 = 14.69N
F(vertical) = mg + Ty - Flift(y-component) = 6.958 + Tsin20 - Flift*sin20
F(horizontal) = F(radial)+ Tx = 14.69 + Tcos20

At this point I don't know how to use the lift to calculate the vertical force, and otherwise cannot find the tension components.

My book does not include any examples of this kind of problem, and the only match I found referred me back here to an unanswered post.

 

[tiny-tim]

welcome to pf!

hi phy221! welcome to pf!

(try using the X² icon just above the Reply box )

You don't know F_lift, so taking horizontal and vertical components of F = ma won't help much

try some other direction for F = ma ​