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As level Non-Uniform Plank question.

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data

    A non-uniform plank of wood AB has length 6m and mass 90kg. The plank is smoothly supported at its two ends A and B, with A and B at the same horizontal level. A woman of mass 60kg stands on the plank at the point C, where AC=2m. The plank is in equilibrium and the magnitudes of the reactions at A and B are equal. the plank is modelled as a non-uniform rod and the woman as a particle.


    (a) the magnitude of the reaction on the blank at B,

    (b) the distance of the centre of mass of the plank from A.

    2. Relevant equations

    Moment = Fx

    3. The attempt at a solution

    For part A i was thinking total down = total up, if thats the case you have 90g+60g = 150g if thats the case would b = 75g as its equilibrium?

    also I would take moments about point A for question (b) however I do no know what i would do from there.

    Help would be appreciated
  2. jcsd
  3. Mar 29, 2010 #2


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    Welcome to PF!

    Hi templarbaza! Welcome to PF! :smile:
    Correct! (well, except that kg would be better! :biggrin:)
    Call the distance from A to the centre of mass "x", and it should work out. :wink:

    What do you get? :smile:
  4. Mar 29, 2010 #3
    well, I did 90x2 + 75x6 = 530

    then Im not quite sure, do you divide it by 150?

    if so i got x = 3.53m
  5. Mar 29, 2010 #4


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    (if you're using x for distance, use * for times)

    Have you drawn the forces?

    What are the three forces, and where are they?
  6. Mar 29, 2010 #5
    hmm im not sure,

    ac = 2m

    c = 60kg

    60 * 2 = 120 (woman x distance from point a)

    75 * 6 = 450 (a x force at point B) < --- not sure about that and from this point onward.

    570 / 120 = x

    x = 4.75m

    Im not sure I know you have a force created by the woman, one by the plank what is the third force?

    If I have the right method but am using the wrong information i would like some more hints =]
    Last edited: Mar 29, 2010
  7. Mar 29, 2010 #6


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    Don't talk like that, it will confuse you …

    it isn't "a force created by the woman", it's the weight of the woman.
    The other two forces are the reaction force at B, and the weight of the plank at its centre of mass.
  8. Mar 29, 2010 #7
    Thanks for the help. so by accounting for the weight of the woman and the reaction force at B and dividing by the weight of the plank would give the Center of Mass (x)
  9. Mar 30, 2010 #8


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    (just got up :zzz: …)
    Yes. :smile:
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