Torque & Equilibrium: Translational & Rotational

[asdasdasd]

Torque/Translational and Rotational Equilibrium

I was given this problem as a quiz in class. Unfortunately, I did not finish it. I decided to try it at home as I need the practice.

Homework Statement

Sorry for the crudely drawn image.
http://image.bayimg.com/lajgkaabb.jpg

Find: $$T, T_2y, T_3y, T_3x$$ given $$T_2y = T_3y$$ and the object is in translational and rotational equilibrium.

Figure of problem also attached.

Homework Equations

Don't think there are any.

The Attempt at a Solution

Sum of all forces is zero.

$$\Sigma x = T_3x + -T\cos30^\circ = 0$$
$$\Sigma y = 2T_2y + T\sin30^\circ - 500N = 0$$

Sum of torque is zero.

$$\Sigma\Gamma = -(4m)(2T_2y) + (1.75m)T_3x + (2m)(500N)$$

Substitution time?

$$T_3x = T\cos30^\circ$$
$$T_2y = \frac{500N - T\sin30^\circ}{2}$$
$$0N = -(4m)(500N - T\sin30^\circ) + (1.75m)(T\cos30^\circ) + 1000N$$
$$0N = -1000N + 3.516T$$

Proposed values

$$T = 284.414N$$
$$T_3x = 246.31N$$
$$T_2y = T_3y = 178.896N$$

I just want to know if I did this correctly. If not, I would greatly appreciated any help. Thanks for taking the time to read this.

 

[asdasdasd]

Sorry to bump my own thread... I just want to know if I did the problem correctly...