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

[ehabmozart]

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..

Homework Equations

The Attempt at a Solution

 

[truesearch]

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?

 

[ehabmozart]

Thanks a lot dude... I owe u big time