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...

 

[Moetasim]

Hello,

I can confirm that your approach to this problem is correct. You correctly identified the equations needed to solve for the unknown tensions and used substitution to solve for them. Your proposed values for T, T_3x, T_2y, and T_3y are also correct. Overall, you have successfully demonstrated an understanding of torque, equilibrium, and how to apply them to solve a problem. Great job! Keep practicing and you will continue to improve your skills in this area.