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asdasdasd

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**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: [tex]T, T_2y, T_3y, T_3x[/tex] given [tex]T_2y = T_3y[/tex] 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.

[tex]\Sigma x = T_3x + -T\cos30^\circ = 0[/tex]

[tex]\Sigma y = 2T_2y + T\sin30^\circ - 500N = 0[/tex]

Sum of torque is zero.

[tex]\Sigma\Gamma = -(4m)(2T_2y) + (1.75m)T_3x + (2m)(500N)[/tex]

Substitution time?

[tex]T_3x = T\cos30^\circ[/tex]

[tex]T_2y = \frac{500N - T\sin30^\circ}{2}[/tex]

[tex]0N = -(4m)(500N - T\sin30^\circ) + (1.75m)(T\cos30^\circ) + 1000N[/tex]

[tex]0N = -1000N + 3.516T[/tex]

Proposed values

[tex]T = 284.414N[/tex]

[tex]T_3x = 246.31N[/tex]

[tex]T_2y = T_3y = 178.896N[/tex]

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.

#### Attachments

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