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Torque and Equilibrium

  1. Oct 25, 2014 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

    T = F*R*sinΘ
    ∑T = 0

    3. 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
     
  2. jcsd
  3. Oct 25, 2014 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Where are you getting 4.75 and 1.4?
     
  4. Oct 25, 2014 #3
    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.
     
  5. Oct 25, 2014 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Isn't it given as 5 m?
     
  6. Oct 25, 2014 #5
    Sorry I was thinking of the last practise version I did. Each version has different values.
     
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