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Torque/Moment of a bent wrench question

  1. Feb 13, 2016 #1
    Hi everyone,
    The problem below kinda confuses me.....i've spend half an hour staring at this problem lol.

    The problem statement, all variables and given/known data:

    Q: A bent wrench is used to apply a moment of 221 Nm to the hexagonal nut. If the applied force F is 507 N and the angle θ is 21°, find the distance d. Answer in metres.

    http://imgur.com/pLjSJkQ

    http://[noparse]http://imgur.com/pLjSJkQ[/noparse] [Broken]

    https://courses.kpu.ca/pluginfile.php/287327/question/questiontext/205374/1/856670/q1.jpg [Broken]


    The attempt at a solution:
    Here is what I tried to do:

    Assuming: clockwise moment = negative.

    First:
    break F into components: 507cos21 = Fx and 507sin21 = Fy.

    Second:
    Since Fy is along the line of 'd' it has zero moment at the "bent pivot" (not at the nut).
    But Fy will exert a moment at the hexagonal nut: so break Fy into components: 507sin21sin28.

    Third:
    find net moment: -(507cos21)*d + (507sin21sin28)*0.3 = -221
    So, d = 0.52m

    But the correct answer given to us is: 0.26m

    I think I might have mad an error with the moment at "the bent pivot". Since "-(507cos21)*d" equals to the moment at the "bent" and not at the Origin(hex nut).....should I shift the moment at the bent to the origin(nut)?
    Or I can think of it as part of the net moment?

    I'm still a bit confused about the Net moment at the Origin(nut), does the Net moment mean the sum of all the moments acted on the body, regardless of where it acts? Or does all the moments have to be on the Origin?

    Thank you all for the generous help.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 13, 2016 #2

    SteamKing

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    This problem is quite simple if you know that M = r × F , where M, r, and F are all vectors and you are taking the cross product of r and F.

    If you know only the basic definition of the moment of a force, it's still easy.

    Take for example this curly wrench:


    http://web.mit.edu/4.441/1_lectures/1_lecture5/wrench1.gif

    The moment arm is 12" between the red arrow, which indicates the applied force, and the center of the nut or bolt being tightened. The shape of the wrench in between these two points is immaterial to how much torque is generated.

    For your particular problem, you need to find the distance between the center of the bolt and the tail of the force vector. Also, you need to figure out the component of the turning force which acts at right angles to this lever arm. Then, you can work back and find the distance d.
     
    Last edited by a moderator: May 7, 2017
  4. Feb 13, 2016 #3

    haruspex

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    The component F sin(21)sin(28) acts through what point? How far is that from the nut?
    The component F cos(21) acts in what direction and is how far from the nut?
    But an easier way (in my view) is to extend the 30cm line out and drop a perpendicular to it from the tip of the wrech where F is applied. What is the angle between that perpendicular and the line of action of F?
     
  5. Feb 13, 2016 #4
    Oh, ive tried to attach an image of the wrench, but it doesnt seem to display properly here, so I added the link http://imgur.com/pLjSJkQ
    of the diagram.
    sry about that.
     
  6. Feb 13, 2016 #5

    haruspex

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    Yes, I followed the link and saw the image. My comments stand.
     
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