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Calculate moment of a special wrench

  1. Feb 18, 2013 #1
    1. The problem statement, all variables and given/known data

    The specialty wrench shown in the figure is designed for access to the hold-down bolt on certain automobile distributors. For the configuration shown where the wrench lies in a vertical plane and a horizontal 200-N force is applied at A, perpendicular to the handle, calculate the moment applied to the bolt at O. For what value of the distance d would the z-component of be zero?

    jb3hig.jpg

    2. Relevant equations

    M = r x F ;

    M= Fd

    3. The attempt at a solution

    Well I succesfully calculated the moment around O as M=-48.6j -9.49k Nm but I failed to calculate the second part of the problem.

    It was asking for d in order to make Mz equal to zero.

    Using M=Fd I have:

    M=√My2+Mz2 = F d

    From that equation I have to find d in order to make Mz zero so I substitute Mz for zero and I calculate te value of d:

    √My2=Fd

    d=My/F=48.6/200=0.24

    But the book gives a value of 74.5 mm, What am I doing wrong?

    Thanks!
     

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    Last edited: Feb 18, 2013
  2. jcsd
  3. Feb 18, 2013 #2
    You could solve this in two different ways. First, you could express r as a function of d, then use the M = r x F to find the dependence on d.

    Or, you could recall that the moment about an axis is proportional to the distance from the axis.
     
  4. Feb 18, 2013 #3
    Ohh, I´m sorry, you are right. I was assuming that d was the moment arm but it´s not, in this problem is the distance d as it´s shown in the picture, what a ridiculous mistake.

    Now I find the correct answer:

    d=70/cos(20)=74,5 mm

    Thank you very much!
     
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