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

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SUMMARY

The angle formed by the chain of a chair-o-plane seat remains constant regardless of the weight of the occupant due to the balance of forces acting on the system. For both a 45 kg child and a 90 kg man, 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). This results in the same angle θ being maintained, as the ratio of these forces remains unchanged. The key equations involved are T cos θ = mg and T sin θ = mv²/r.

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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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