How Does Chair Rotation Affect String Tension in Physics?

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The discussion focuses on calculating the increase in tension in a string holding a bob in a rotating chair. Initially, the tension when the bob is hanging vertically is calculated to be 196N. The user attempts to find the angle theta for the rotating scenario, estimating it at 13.7 degrees, leading to a calculated tension of 201.7N. However, it is noted that the angular velocity or frequency of the chair's rotation is essential for accurately determining theta and the resulting tension. The conversation emphasizes the need for precise measurements and calculations in physics problems involving rotational motion.
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Calculate the increase in tension in the string holding up the bob in the rotating chair. Calculate the tension when the bob is hanging vertically and the tension when the chair is rotating. H=65.3cm Ro=32cm The bob is 20.0g

I found that the Tension in the string when the bob is hanging vertically to be

T1=Fg=196N

I drew a free body diagram and my equations are Tcos(theta)=mg and Tsin(theta)=m(v^2/r)

So I would find the Tension in the string when the chair is rotation by using the equations

T=mg/cos(theta)

I am not sure how to find theta. I know the adj side is equal to the height 65.3, but how do I find the radius?
 

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Can anyone help on this one?
 
I found that R=16

I did this just by looking at the picture. Ro=32 and it looks like the plumb bob is about half of that to the right.

So, I found the angle to be 13.7 degrees

T=mg/cos(13.7) T=201.7 The difference in T=5.80N

Does this look right?
 
Ok, that answer was wrong. Does anyone have any suggestions?
 
You need to know how fast is the chair rotation (angular velocity or period or frequency).
The angle depends on this.
You can find the angle writing Newton's second law for the circular motion of the bob.
 
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