# Rotation chair and tension

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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## Answers and Replies

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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.