Farmyard Gate - Equillibrium

  • #1

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
where relative to the center are the hinges and the wire located?
 
  • #3
tiny-tim
Science Advisor
Homework Helper
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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! :smile:

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? :smile:

(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! :redface:)
 
  • #4
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 |{----------
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
251
ok … so which point on the line DAB should you take moments about to find the tension when the force at A is vertical? :smile:
 

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