Tension and centripital motion help

[erogers4]

Two identical blocks are tied together with a string and placed along the same radius of a turntable that is spinning about its center. The inner block is 3 cm from the center and the outer block is 6 cm from the center. The coefficient of static friction between the turntable and the blocks is µs = 0.74, and the string is taut.

I have determined that w = 12.7 rad/s

Now suppose that the blocks each have a mass m = 35 g. For the value of w you just found, what is the tension in the string?

For some reason, I cannot seem to get the right answer. SOMEONE PLEASE HELP!

 

[Doc Al]

Show your work and how you solved for the tension and we can take a look.
The same equations used to solve for $\omega$ (the maximum rotational speed without slipping) will include the tension.

 

[erogers4]

my equations i used were:
1) T - umg = m R1 w^2
2) -T - umg = m R2 w^2

i was able to get w, but then i plug values back in and its not accepting my answer for T as being correct. i have no idea what I am doing wrong. please help!

 

[Doc Al]

For one thing, your signs are messed up in those equations. Choose a sign convention: for example, make towards the center positive, away from the center negative. Rewrite those equations accordingly. (The way they are written now, $\omega^2$ is negative!)

 

[erogers4]

ok i realized i typed in the wrong ones...i had those at first, the new ones are
1) -T + umg = m r1 w^2
2) T + umg = m r2 w^2

i believe that is how i got 12.7 for w (i have so much work here and half of it is wrong, I am not sure which is which anymore). I just tried solving for T though and it is still not right. ah I am so confused now!

 

[erogers4]

Ok maybe those equations aren't right either...I can't seem to get the 12.7 for w again, tho I know that is right. I have no idea what I'm doing anymore!

 

[Doc Al]

Those equations are correct. Show how you solved for T and what you got.

(To find $\omega$, start by adding those two equations.)

 

[erogers4]

to find T i had:

T = umg - m r1 w^2
as well as
T = m r2 w^2 -umg

m=.035kg
r1=.03m
r2=.06m
w=12.7 rad/sec
u=.74
g=9.81

i plug those in and get
T=.0847

which apparently is right...i had that before i don't know y it wouldn't take it as being correct...thanks for all you help!