Carnival Swing Question, I am severely stuck

[star33]

Homework Statement

A “swing” ride at a carnival consists of chairs that are swung in
a circle by 3.0 m cables attached to a vertical rotating pole, as the
drawing shows. Suppose the total mass of a chair and its occupant is
50.0 kg.
(2.a) Plot the free body diagram of the chair and its occupant.
(2.b) Determine the tension T in the cable attached to the chair
when its velocity is 3.46 m/s. [Hint: You may need to solve a
quadratic equation to find θ.]

Relevant Equations

centripital force=tension
mg=tension(costheta)

I found the x and y components and then divided the two equations to see if I can solve for the angle but that did not work. I have been at this for two hours, please help me.

 

[BvU]

Please post your work. Did you come to a quadratic equation?

 

[star33]

No I did not, that is the part I am having trouble with. Could you please help me with it?

 

[kuruman]

No I did not, that is the part I am having trouble with. Could you please help me with it?

Go back to part (2.a).
Write Newton's second law for the system consisting of the chair and the occupant.
Post your work.

 

[haruspex]

Relevant Equations: centripital force=tension

Not in this arrangement. Which way does the centripetal force need to act? Which way does the tension act?

 

[Lnewqban]

(2.a) Plot the free body diagram of the chair and its occupant.

I found the x and y components and then divided the two equations to see if I can solve for the angle but that did not work. I have been at this for two hours, please help me.

Welcome, @star33 !

Could you please show us your free body diagram, and the x and y components, and the two equations?