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Math Help - Tension Statics Problem

  1. #1
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    Question Tension Statics Problem

    1. The problem statement, all variables and given/known data
    See figure, "CraneProblem".


    2. Relevant equations:

    Sum Fx = 0,
    Sum Fy = 0.


    3. The attempt at a solution

    See figure, "CraneAttempt". I said for the maximum weight to be held the ropes must be at maximum tension then used Fy: to compute m1 and m2. My solution causes problems in the equilibrium of the X-Components of the tensions. Any ideas?
    Attached Thumbnails Attached Thumbnails Tension Statics Problem-craneproblem.jpg   Tension Statics Problem-craneattempt.jpg  
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello jegues
    Quote Originally Posted by jegues View Post
    1. The problem statement, all variables and given/known data
    See figure, "CraneProblem".


    2. Relevant equations:

    Sum Fx = 0,
    Sum Fy = 0.


    3. The attempt at a solution

    See figure, "CraneAttempt". I said for the maximum weight to be held the ropes must be at maximum tension then used Fy: to compute m1 and m2. My solution causes problems in the equilibrium of the X-Components of the tensions. Any ideas?
    Your equations are fine. I think you then need to work out which cable has the greatest tension. So, using:
    \cos45^o=\sin45^o =\frac{1}{\sqrt{2}}

    \cos30^o = \frac{\sqrt3}{2}

    \sin30^o = \frac12
    we get, by eliminating T_5:
    T_3\cos45^o = T_4\cos30^o
    \Rightarrow T_3 =T_4\sqrt{\frac32}

    \Rightarrow T_3>T_4
    and
    T_5 = T_3\frac{1}{\sqrt2}

    \Rightarrow T_3>T_5
    Similarly
    T_3 > T_1 and T_4 > T_2
    So T_3 is the greatest tension. The maximum value of the combined masses occurs, then, when T_3 = 100,000 N.

    Substitute this value into the equations to work out T_1 and hence M_1. Then work out T_4; and hence T_2 and M_2.

    Grandad
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