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Static Equillibrium

  1. Feb 8, 2010 #1
    Hi everyone, first time post at physics forums, I hope to help out some people with calc and I hope to discuss some physics topics too! But however I have a homework question in MECH 234.

    1. The problem statement, all variables and given/known data

    Find Tac + Tbc from the given picture:


    2. Relevant equations

    ΣFx = 0
    ΣFy = 0

    3. The attempt at a solution

    Well first, since 500N is being pulled on the x axis-

    ΣFx = 0 = Tac*sin(50)+Tbc*sin(30) - 500

    500 = Tac*sin(50)+Tbc*sin(30)

    The right side is the sum of all the Fx components and they must be equal to zero.

    ΣFy = 0 = Tac*cos(50)+Tbc*cos(30)

    The right side is the sum of all the Fy components and they must be equal to zero.

    When I try to solve the two equations (2 unkowns 2 equations) I just get crazy numbers. I do not know what mistake I could be making otherwise except the angles might be wrong. Or perhaps I should be using the law of cosines or sines?
  2. jcsd
  3. Feb 8, 2010 #2
    You may be making the mistake in the equation you have for the y dimension. You have that the sum of all y forces is zero, which is correct. However, you may have made your mistake by not setting Tac*cos(50) equal to Tbc*cos(30). Did you mistakingly say Tac*cos(50) equals -Tbc*cos(30)? Also, put up the numbers you got so it is easier to find where you went wrong.
  4. Feb 8, 2010 #3
    Well I solved for the equations:

    0 = Tac*cos(50)+Tbc*cos(30)
    500 = Tac*sin(50)+Tbc*sin(30)

    and got

    Tac ~ 1.98
    Tbc ~ -199

    I did not know that you need to set Tac*cos(50) equal to Tbc*cos(30).

    Why do they have to be equal? Is it because there is no y component in the 500lb force; therefore, both components need to be equal to each other for equilibrium?

    My answer for solving the system of equations-

    500 = Tac*sin(50)+Tbc*sin(30)
    Tac*cos(50) = Tbc*cos(30)

    Tbc= 326.3518 N
    Tac= 439.6926 N

    It is correct. And I would like to thank you in advance.
    Last edited: Feb 8, 2010
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