Carnival Swing Question, I am severely stuck

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The discussion revolves around solving a physics problem related to a carnival swing, focusing on the application of Newton's second law and the analysis of forces acting on the chair and its occupant. The user is struggling to derive the angle from the x and y components of the forces and has not reached a quadratic equation, which is crucial for solving the problem. Participants are encouraging the user to share their free body diagram and the equations they have formulated to provide better assistance. The conversation emphasizes the importance of visualizing the forces and correctly applying relevant equations, such as centripetal force and tension. Overall, the user seeks guidance to move past their current impasse in the problem-solving process.
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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.
Screenshot 2023-12-16 at 1.01.55 PM.png
 
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Please post your work. Did you come to a quadratic equation?
 
No I did not, that is the part I am having trouble with. Could you please help me with it?
 
star33 said:
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.
 
star33 said:
Relevant Equations: centripital force=tension
Not in this arrangement. Which way does the centripetal force need to act? Which way does the tension act?
 
star33 said:
(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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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