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Trouble Determining Moment Arm (aka Lever Arm)

  1. Mar 3, 2016 #1
    1. The problem statement, all variables and given/known data
    1.png

    2. Relevant equations
    ΣM=Στ

    3. The attempt at a solution
    I know how to get the net torque about point P, but I am having difficulty determining where the moment arms for each force should be. I did 9 simpler questions before this no problem, but this diagram is a bit more complicated and I'm having trouble with it. The last three questions I have to do are all exactly the same (this one) with different numbers, so some help would be greatly appreciated!

    I know the moment arm is the perpendicular distance from the line of action of the force to the point of rotation.

    I am confused as how to find the length of the moment arms in this particular diagram. I think they should look like this (orange and blue lines)
    1.png

    But I am lost as to how to get their lengths (if where I have them is even correct).
     
  2. jcsd
  3. Mar 3, 2016 #2
    Hi,

    Perhaps you could try to divide the forces F2 and F1 in the x and y directions.

    Such that F2x = F2cos(A2), F2y = F2sin(A2), F1x = F1cos(A1), and F1y = F1sin(A1).

    Hence, Your free body diagram would look a little like the attached picture.

    Hope this answers your question!
     

    Attached Files:

  4. Mar 4, 2016 #3

    Nidum

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    Look at the point where your blue line crosses the horizontal line at the bottom of the rectangle .

    What do you know about the two acute angles there ?

    What do you know about the sum of the angles in right angle triangles ?.
     
    Last edited: Mar 4, 2016
  5. Mar 5, 2016 #4
    I've tried this a few time and I haven't been able to get the correct answer :(
    Do you spot a mistake I could have made?
    If you can't read my writing I can type it out!
    IMG_0270.jpg
     
  6. Mar 5, 2016 #5
    I'm not sure, are they supposed to be the same?

    They add up to 180 degrees.
     
  7. Mar 5, 2016 #6
    This is messy, sorry, but I'm at this point in trying to figure the question out!
    IMG_0271.jpg
     
    Last edited: Mar 5, 2016
  8. Mar 5, 2016 #7

    Nidum

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    Yes - they are the same . So what is the angle between your blue line and the left vertical line of the rectangle at point P ?
     
  9. Mar 5, 2016 #8
    38.3 degrees
     
  10. Mar 5, 2016 #9

    Nidum

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    Yes - that angle and angle A1 are the same . Quick bit of trig now will give you length of blue line ?
     
  11. Mar 5, 2016 #10

    Nidum

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    Hint : Work out the base length of the triangle below point P .
     
  12. Mar 5, 2016 #11
    Tried it this way, still not getting correct answer
    IMG_0272.jpg
     
  13. Mar 5, 2016 #12

    Nidum

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    1-png.96777.png

    This was your best diagram . Put in the actual dimensions and angles as given and add those that you have worked out so far .

    Label all points where lines meet or cross . Simple a , b , c --- will suffice .
     
    Last edited: Mar 5, 2016
  14. Mar 5, 2016 #13
    I eventually solved it using the first method I tried (breaking into x and y components.
    Thanks for your help.
    IMG_0275.jpg
     
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