What is the tension required for the crosspiece in an A-frame structure?

[iPromise]

∑

Homework Statement

You are designing the crosspiece for the A-frame structure in the figure below. Beams AB and AC are 5.00 m long and have a mass of 375.0 kg each. How much tension must the crosspiece EF withstand? Assume that the mass of the crosspiece and the friction at points B and C are negligible.

http://oi57.tinypic.com/2zfq4y8.jpg

Homework Equations

T = F*R*sinΘ
∑T = 0

The Attempt at a Solution

I took the first half of the frame into consideration. I chose point A to be my pivot point. There are three forces acting on the first-half of the frame:

http://oi59.tinypic.com/fu7sw0.jpg

My initial equation:

(N)(4.75)(cosΘ) - (Mg)(2.375)cosΘ = (T)(1.4)

Θ = sin-1 ( 2.2 / 4.75 )
= 27.59

N = the force of gravity of the first half of the structure
= Mg = 335 * 9.81

I solve for T:

T = 4941.08

The answer: 8650

 

[Doc Al]

(N)(4.75)(cosΘ) - (Mg)(2.375)cosΘ = (T)(1.4)

Where are you getting 4.75 and 1.4?

 

[iPromise]

4.75 is the length of the ladder. 1.4 was the radius from the pivot point. That was my mistake, 1.4 is NOT the radius, 0.8 is.

 

[Doc Al]

4.75 is the length of the ladder.

Isn't it given as 5 m?

 

[iPromise]

Sorry I was thinking of the last practise version I did. Each version has different values.