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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.

    2. Relevant equations

    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.....
    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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