Why Is the Angle the Same for Different Weights in a Chair-O-Plane?

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The discussion centers on the physics of a chair-o-plane, specifically the angle formed by the chains supporting the seats when occupied by different weights. Despite varying weights, the angle remains the same due to the balance of forces acting on the system. The vertical component of tension (T cos θ) equals the gravitational force (mg), while the horizontal component (T sin θ) relates to the centripetal force (mv²/r). By combining these equations, it becomes clear that the angle θ is determined by the ratio of forces rather than the mass alone. Thus, the angle remains constant for different weights in this scenario.
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Homework Statement


The chair o plan seats are supported by chains hung from a circular structure. What angle to the vertical will be formed by the chain of a chair-o-plane seat is occupied by a 45 kg child if the tension is 550 N... I was able to solve this one.. THe question I need a help in is this: A nearby chair is occupied by a 90kg man. Explain why the angle formed by the chain will be the same as for the child... Mathematically, i feel this question is in apropiate.. If we say T cos theta is (mg) so by altering m , the angle changes too .. Isn't it.. if not, I need the correct answer..


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The Attempt at a Solution

 
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I think you will find that you had to use 2 equations to find the angle θ.
Vertical component of tension = TCosθ = mg
and horizontal component TSinθ = mv^2/r
Put these together (to get Tanθ)... see what happens?
 
Thanks a lot dude... I owe u big time
 

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