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Forces: Moment

  1. May 18, 2007 #1
    1. The problem statement, all variables and given/known data
    In this problem, take g = 10 m s-2.
    A uniform plank of length 14 m long and mass 20 kg is being supported at B and C as shown above.
    Two boys X and Y of masses 20 kg and 50 kg respectively are right on top of the supports.
    X starts to walk towards A and Y walks towards D at the same time.
    If both boys walk at 1.0 m s-1, the plank begins to overturn after how many seconds?

    2. Relevant equations
    Clockwise moment = anticlockwise moment

    3. The attempt at a solution
    The answer given is 4seconds.
    i can't work it out,really need help.
    Need a little hint please.
    Last edited: May 19, 2007
  2. jcsd
  3. May 19, 2007 #2
    re: Moment Problem

    Imagine support C is not there. Imagine each boy has walked for 1 second. Each boy exerts a moment around B equal to is weight times his distance from B. If BoyY's moment is larger, the plank will want to rotate CW. But the plank doesn't rotate because support C is there. Will BoyX's moment eventually become larger? If so when?

    Now do the same thing imagining that support B is not there.
  4. May 19, 2007 #3
    Sup flood, this is what I got:

    F_y equilibrium gives: B + C = 90g
    Moment equilibrium about B gives: t = (C - 60g)/ 7.5g,

    Where B and C are the reactions at B and C, and t is the time after X and Y start moving.

    Recall that the reactions are given by:

    B + C = 90g

    I figured that since Y is heavier, the beam will overturn when all the weights are centered at C i.e. when B = 0 and C = 90. Subbing this into the moment eqbm equation, we get:

    t = 30g/ 7.5g = 4 s

    Which is the answer yea? How'd you get 1 s? Anyhows... yea lemme know if that helped.

  5. May 19, 2007 #4
    Yea kenny lee your right.
    Thanks alot.
    Last edited: May 19, 2007
  6. May 20, 2007 #5
    Glad to be of help =)
  7. May 20, 2007 #6
    But how did you get 7.5g anyway?
  8. May 20, 2007 #7
    I've attached my working. Its Jpeg. Um you have a look, see if it makes sense. (or if its even right).

    G luck

    Attached Files:

  9. May 20, 2007 #8
    Thanks a zillion for ya effort and time.
    God bless..
    Last edited: May 20, 2007
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