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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
T = F*R*sinΘ
∑T = 0
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
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