Circular motion - Which string breaks first?

[Raishiin]

Homework Statement

Basically, three different masses hanging on three strings of different lengths all different distances from the axis of rotation. They have a maximum tensile strength of 450 Newtons. I have to solve in variable form first, and however... Well, okay. Just check the image below.

http://i44.tinypic.com/ae4egk.jpg

I just need to find an equation where I can vary the rotational speed and solve for the tension. Despite what I show in the image, for step two I really seem to need an equation where when given all the variables you can solve the function by changing "N" until you see it hits 450 Newtons and the string breaks. The angle theta changes the radius which changes the velocity which then changes the acceleration and centripetal force so things just go bad really fast for me.

Homework Equations

v = (2piR/N)
a = v^2/r
F(c) = mv^2/r

The Attempt at a Solution

Well, based on the image I drew and posted... The corrected radius is the original radius plus the string length multiplied by the sin of theta. Using all that I wind up finding two functions from that picture that I think could apply for the tensions... But I'm making a screwy mistake somewhere in one of these. (m*g*cos(theta) or just m*g the whole time?)

T = mgcos(theta) + 4mpi^2(R+Lsin(theta)/N^2 = 450
Or
T = mg + 4mpi^2(R+Lsin(theta))/N^2 = 450

If anyone can help me, that'd be great. I feel like such an idiot because this was on my last test. (Though my professor honestly didn't prepare us for questions like this. None of the homework or worksheets was nearly this hard... -_-)

Oh! I accidentally labeled the opposite "H" in the diagram. I meant to say "O" for opposite. My bad...

 

[anathema]

It seems like you are trying to find an equation that relates the rotational speed, tension, and other variables in this system. First, make sure you have a clear understanding of the variables involved and their relationships. From the diagram, it looks like the system consists of three masses hanging on strings of different lengths, with a maximum tensile strength of 450 Newtons. The angle theta changes the radius, which affects the velocity, acceleration, and centripetal force.

In order to find an equation that relates all of these variables, you can use the equations you listed in the "Homework Equations" section. The first equation, v = (2piR/N), relates the rotational speed (N) to the radius (R). The second equation, a = v^2/r, relates the velocity (v) to the acceleration (a) and radius (r). And the third equation, F(c) = mv^2/r, relates the mass (m), velocity (v), and radius (r) to the centripetal force (F(c)).

Using these equations, you can manipulate them to solve for the tension (T) in terms of the other variables. For example, using the third equation, you can solve for T by setting F(c) = 450 Newtons and substituting in the values for m, v, and r in terms of the other variables. This will give you an equation that relates T to N, R, and theta. You can also try using the first two equations together to eliminate the velocity and solve for T in terms of N, R, and theta.

It's important to carefully consider the units and make sure they are consistent throughout your equations. Also, make sure you are using the correct values for the variables, as it looks like there may be some confusion with the labels in your diagram.

I hope this helps and good luck with your problem solving! Remember, practice makes perfect and don't be too hard on yourself if you make mistakes. We all learn from our mistakes and they help us improve. Keep up the good work!