Find Mass and Speed given Tension and Angle

[geek96boolea10]

Homework Statement

Imagine one of those amusement park rides where you have a large rotating disc with seats hung by chains around it. As the disc spins, the seats also spin whilst rising up as well. The question asks for all answers to be written given the constants L, the length of the chain, T, the tension of the chain, and Theta, the angle above the horizontal that the chain is at. Given that the diameter of the disc is 2L, the chain is L, the angle is Theta, the tension between seat and disc is T, and the speed of rotation is constant, determine the mass of a seat and the speed of that seat.

Homework Equations

I'm pretty sure F=mv2/r is important. Lcos(theta) and Lsin(theta) are also useful in some way.

The Attempt at a Solution

My solution attempt was to simply expand F=mv2/r, replacing what I could. I ended up with the equation:
mv2 = T/(L+Lcos(theta)) which can be changed to m= or v2= pretty easily. However, they both include either m or v, which are not allowed since they aren't given constants. I'm sure that I've been using the wrong equation or that I'm missing some fundamental equality that would make this super easy - help!

 

[Nathanael]

and Theta, the angle above the horizontal that the chain is at

The angle above the horizontal? Do you mean the angle below the horizontal? (I just want to make sure we're imagining the same ride.)

 

[haruspex]

the angle above the horizontal that the chain is at

They won't be above the horizontal. Did you mean below horizontal, or maybe angle from vertical?

I'm pretty sure F=mv2/r is important.

Yes, but what do v and r represent there in the context of this question?