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Statics Problem Submerged Object

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    A 0.5 x 0.8m gate AB is located at the bottomof a ank filled with water. The gate is hinged along its top edge A and rests on a frictionless stop at B. Determine the reactions at A and B when cable BCD is slack.
    Statics4.jpg


    2. Relevant equations
    Fx=0
    Fy=0


    3. The attempt at a solution
    I thought I would have to find the pressure of the water would be the x component, and then the weght of the water would be for the y component....

    Since all of the widths are the same I figured they would null each other out because if they weren't the same water would either over flow under B and A.

    Pressure=(1/2)bh*density=(1/2)*.93*.64*1000=297.6 kg (not a force)
    Weight=Area of triangle+area of rectangle
    =(1/2)bh+bh=((1/2)*.64*.48*1000)+(.64*.93*1000)=748.8 kg(not a force)

    I don't understand excatly what the next step is what I tried doing was making Fx and Fy equations and solve for one.....but i dont know how to turn kg into N, because when I multiply by gravity I get a huge number which gives me the wrong answer.....

    Here is my work drawn out on my picture.....
    Statics4-WOrk.jpg
    Orange triangle is the pressure
    The purple square and blue triangle is the weight. Does this make sense? Or am I in the wrong direction
     
  2. jcsd
  3. Oct 17, 2009 #2
    I have a better understanding now I believe is this the correct value for P and W......

    P=width*specfic weight*hieght*height*(1/2)
    =.5m*(9800N/m^3)*.93 m* .93m *.5m=2119.005 N

    W=(area of triangle+area of rectangle)*9800
    =(.5*.64*.48)+(.64*.45)=.4416*9800=4327.68 N
     
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