Pendulum tension in rotating reference frame

[knightcydonia]

Homework Statement

A student is in a rotating chair with a pendulum hanging down in the middle of the rotation. . I need to calculate the difference in tension when the bob is hanging vertically and when the chair is rotating. The length of the bob and string is 65.3 cm. The radius of the rotation is 32 cm and the bob weighs 20.0 g and the chair completes a rotation every 3 sec.

Homework Equations

F=ma
T=mg
F=m(v^2/r)
ac=v^2/r
v=(2piR)/T

The Attempt at a Solution

The tension when it is vertical and not rotating would just be T=mg or .196N. When the chair is rotating I get confused. To me it seems all I have to do is find the angle the bob makes with the vertical and multiply this to the tension of the vertical (but I can't find the angle). However, since the chair is rotating I'm not sure how this effects tension. I'm not sure if centripetal acceleration has anything to do with it. I'm not even sure how to make the free body diagram. I know mg and T act on the bob in opposite directions and a fictitious force is pulling the bob outward.

Thanks for the help.

 

[tiny-tim]

hi knightcydonia!

if you're using the corotating frame, then there's no acceleration at all,

so you can treat it as an ordinary statics problem (with the extra, centrifugal, force) …

just do a free body diagram as usual

 

[knightcydonia]

sorry, but for the free body diagram T and mg are opposite and the bob is unknown degrees from vertical. What is causing the bob to move outward? the fictitious centrifugal force? I don't know how to find the angle...? sorry

 

[tiny-tim]

What is causing the bob to move outward? the fictitious centrifugal force?

yes!

pretend it's a fictitious horizontal rope, and put it in the diagram …

now proceed as usual (free body diagram or vector triangle )

 

[knightcydonia]

Thank you for speedy replies and help!