Find tensions in two strings supporting a rotating mass

[joemama69]

Homework Statement

A shaft is set up in the vertical direction. Two strings are attached to a mass m, the shaft is rotates so that the tangential velocity of m is 3.10 m/s

a) Find tension of string 1 & 2

Homework Equations

The Attempt at a Solution

First I found the acceleration

a = v²/r = 3.1²/1.25 = 2.48 m/s²

F_a = ma = 1.75*2.48 = 4.34 N

I then took it into components

$$\sum$$F_x = F_a - T₁sin$$\theta$$ - T₂sin$$\theta$$ = 0 = 4.34 - T₁sin$$30$$ - T₂sin$$30$$


$$\sum$$F_y = T₁cos30 - mgT₂cos30 = 0

are these correct i would just solve for the Ts here on after

 

[joemama69]

i thin F_y = T₁ - T₂ - mgcos30 = 0