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Weight On Hanging Supports Question

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    The figure below shows a weight, W, supported by two wires, the stresses n the wires AB and AC are not to exceed 100M N/m^2 and 150 N/m^2 resp. The X-sectional Area of AB is 400 mm^2 and AC is 200 mm^2. you are required to calculate the largest load which can be supposted by the two wires.


    http://img130.imageshack.us/img130/9804/26382989.jpg [Broken]


    in summary

    P(ab)= 100 x 10^6 N/m^2
    P(ac)= 150 x 10^6 N/m^2
    A(ab)= 400mm^2 => 0.0004 m^2
    A(ac)= 200mm^2 => 0.0002 m^2

    2. Relevant equations

    P = T/A
    => T = PA

    3. The attempt at a solution

    since system is in equillibrium summation of horizontal forces:

    Fh =0
    T(ac) Cos45 = T(ab) Cos30
    T(ac)= 1.225 T(ab)

    since system is in equillibrium summation of vertical forces:

    Fv = 0

    T(ab) Sin30 + T(ac) Sin45 - W = 0

    but
    T(ac) = 1.225 T(ab)

    so
    T(ab) Sin30 + 1.225 T(ab) Sin45 = W
    1.336 T(ab) = W

    ____________________

    T = PA

    T(ab) = P(ab) x A(ab)

    T(ab) = 100 x 10^6 N/m^2 X 0.0004 m^2
    T(ab) = 40000 N

    but

    1.336 T (ab) = W
    W = 53.440 KN


    Out of curiosity i checked to see if i got the same answer if i used an equation in terms of W and T(ac)...

    T(ab) = 0.816 T(ac)

    1.115 T(ac) = W

    T(ac) = 150 x 10^6 N/m^2 X 0.0002 m^2
    T(ac) = 30000 N

    1.115 T(ac) = W
    W = 1.115 (30000)
    W = 33.450 KN


    i dont see why i am getting 2 different values for the Weights... the math appears flawless... or is it o_O
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 11, 2009 #2

    stewartcs

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    Your math looks fine...however, you are missing the point of the problem.

    Hint: What is the stress in each wire if you use a W of 53.440 kN? Are they acceptable? What is the stress in each wire if you use a W of 33.450 kN? Are they acceptable?

    CS
     
    Last edited by a moderator: May 4, 2017
  4. Nov 11, 2009 #3

    nvn

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    Homework Helper

    thelovemonkey: You are doing well; however, your solution contains a mistake: 1.336 is incorrect. Try that again.
     
  5. Nov 11, 2009 #4

    stewartcs

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    Science Advisor

    I think he just made a typo... (1.336 versus 1.366)...his equations look right...

    CS
     
  6. Nov 11, 2009 #5
    omg i got it... the 54 blah blah blah Newtons is too much for the wire AC to handle as in it produced a pressure over 150 X 10^6 N/m^2... i did it on my calc and am too tired to do it again and post the answer.

    thanks guys... you're the best (Y)
    extra kudos to stewartcs
     
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