Solve Rotating Mass Tensions: Find Tup and Tlow

[Ironmely]

Homework Statement

A mass m is connected to a vertical axle by two strings of length l each making a 45 degree angle with the axle. Both the axle and mass are rotating with angular velocity w. Gravity is pointed downward. Find the tension in the upper string Tup and the tension in the lower string Tlow.
(clue: if lw^2= sqrt(2)g then Tup=sqrt(2)mg

Homework Equations

Fcp=(mv^2)/r
v=wr

The Attempt at a Solution

when considering the y-axis:
Tup/sqrt(2)= Tlow(sqrt) + mg
when considering the x-axis:
Tup/sqrt(2) + Tlow/sqrt(2)= Fcp
Tup/sqrt(2) + Tlow/sqrt(2)= mlw^2

add the equations and then solve for Tup

I think I'm making a mistake when looking at the x-axis, the tension must come from the centripetal force but I am wondering if I'm stating that correctly. I was also thinking about the x-components of Tup and Tlow adding only to the x-component of Fcp but Fcp should be pointed radially towards the axle and also be perpeniduclar to it so then x-component of Fcp is Fcp...Am I making a wrong assumption somewhere here?
Thank you

 

[Ironmely]

Oh, sorry, I figured it out, r in (mv^2)/r is not l but l/sqrt(2)