How to Calculate Tension in a Hinged Gate with an Off-Center Load

[kontroll2007]

Homework Statement

A gate 4.00 m wide and 2.00 m high weighs 528 N. Its center of gravity is at its center, and it is hinged at A and B. To relieve the strain on the top hinge, a wire CD is connected to the gate at an angle of 30 degrees. The tension in CD is increased until the horizontal force at hinge A is zero. What is the tension in wire CD?

Homework Equations

ΣF=0
Στ=0
τ=r*F

The Attempt at a Solution

Fx=Tension(cos(30))
Fy + Tension(sin(30))=528
Tension(sin30)(4m)=528(2m)
Tension= 528N
This is very wrong, I am so lost and confused please help.

 

[dumdum000333]

where relative to the center are the hinges and the wire located?

 

[tiny-tim]

Homework Statement

A gate 4.00 m wide and 2.00 m high weighs 528 N. Its center of gravity is at its center, and it is hinged at A and B. To relieve the strain on the top hinge, a wire CD is connected to the gate at an angle of 30 degrees. The tension in CD is increased until the horizontal force at hinge A is zero. What is the tension in wire CD?

Hi kontroll2007!

Hint: if the horizontal force at A is zero, then that means the total force at A is vertical.

So if you take moments about any point on the vertical line through A, the contribution from A will be zero.

Does that help?

(erm … we can't help you any more until you tell us where C and D are … they're obviously not the other two corners of the gate! )

 

[kontroll2007]

Sorry, but they would not let me put a link to the picture in the post. Ok D is above A on a post while C is on the side opposite the hinges.
|D
|
A |{---------- C
|| |
B |{----------

 

[tiny-tim]

ok … so which point on the line DAB should you take moments about to find the tension when the force at A is vertical?