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Centroid of an area

  1. Nov 23, 2015 #1
    1. The problem statement, all variables and given/known data
    total area = (75x175) +(100x175) +(0.5x50x175) -(π/4 x100x100) = 27964

    my centroid for y = (75x175)(87.5) + (100x175)(87.5) +(0.5x150x75)(25)
    -(π/4 x100x100) (175 - (4(100)/3π) ) / 27964 = 97.13

    my centroid for x = (75x175)(37.5) +(100x175) (125) + (0.5x50x175)(225)-(π/4 x100x100)(175 - (4(100)/3π) ) / 27964 = 37.26 , but the ans given is x = 102 , y= 62.5 , which part of my working is wrong ?
    p/s : i have divided the areas into 4 parts , the first is the (75x175) reactangle , second is (100x175) trianlgle , fourth is -(π/4 x100x100) , the third is the triangle (0.5x50x175)

    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 23, 2015 #2

    SteamKing

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    You have a mistake here. The triangle has dimensions of base = 150 x height = 75
    You have the correct dimensions of the triangle here and the correct moment arm, but you are dividing by the incorrect area.
    You have used the wrong dimensions for the triangle here, but you have the correct x-bar distance.
    You are also dividing by the incorrect area again.
    You could have combined rectangles I and II into one large rectangle and saved some calculation.

    You should always double-check your work to eliminate silly mistakes, like what happened with the dimensions of the triangle.

    Note: My calculations show x-bar = 118.28 mm; y-bar = 56.52 mm
     
    Last edited: Nov 23, 2015
  4. Nov 23, 2015 #3
    My ans is x = 108.3 , y = 61.3 after changing 50 to 150, is my ans wrong?
     
  5. Nov 23, 2015 #4

    SteamKing

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    It's not clear. Why don't you post your revised calculations?
     
  6. Nov 23, 2015 #5
    total area = (75x175) +(100x175) +(0.5x50x75) -(π/4 x100x100) = 35464

    my centroid for y = (75x175)(87.5) + (100x175)(87.5) +(0.5x150x75)(25)
    -(π/4 x100x100) (175 - (4(100)/3π) ) / 35464 = 61.36

    my centroid for x = (75x175)(37.5) +(100x175) (125) + (0.5x50x175)(225)-(π/4 x100x100)(175 - (4(100)/3π) ) / 35464 = 108.3
     
  7. Nov 23, 2015 #6

    SteamKing

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    You have the wrong dimensions for the end triangle here. It is L = 150 mm, H = 75 mm
    You have used the correct dimensions of the end triangle here to calculate the moment, and you are dividing by the incorrect area carried over from the step above.
    For some reason, you are showing the wrong dimensions of the end triangle here in calculating the moment. The triangle should be L = 150 mm, H = 75 mm
    Also, you are dividing by the incorrect area calculated in step one.

    You're still not checking your work to eliminate silly mistakes, like using the incorrect dimensions of the end triangle.

    Please re-do your calculations.

    P.S.: I found a mistake in my own calculations. My calculations for the centroid location now agree with the values shown for x-bar and y-bar in the image attached to the OP.
     
  8. Nov 23, 2015 #7
    (75x175) +(100x175) +(0.5x150x75) -(π/4 x100x100) = 35464

    my centroid for y = (75x175)(87.5) + (100x175)(87.5) +(0.5x150x75)(25)
    -(π/4 x100x100) (175 - (4(100)/3π) ) / 35464 = 61.36

    my centroid for x = (75x175)(37.5) +(100x175) (125) + (0.5x150x75)(225)-(π/4 x100x100)(175 - (4(100)/3π) ) / 35464 = 108.3
    i made the typo..
     
  9. Nov 23, 2015 #8

    SteamKing

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    This calculation is still incorrect. Did you even bother to check the arithmetic after changing the dimensions of the triangle?
    The centroidal locations will not be correct until you calculate the correct area for the figure. Get the first step right.
     
  10. Nov 23, 2015 #9
    Sometimes the easiest way to solve a problem is to translate it into symbolic expressions and equations and then apply algebraic solution methods.

    Less typo and use the help of computer for final algebraic solution. This also helps you to make sure your expression is correct without worrying about your calculation error.
     
  11. Nov 23, 2015 #10

    SteamKing

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    It's not clear how this would help the OP. The problem cannot be solved by algebraic manipulation; it must be solved by the old-fashioned direct grunt work of arithmetic.

    Besides, if you can't get the arithmetic to work, how are you going to get the algebra right? :wink:
     
  12. Nov 23, 2015 #11
    I guess this is easy for me to see.
    ae(a/2) + be(b/2+a) + cd/2(c/3+a+b)-πr2//4(a+r/3) = x(ea+be+cd/2+πr2/4)
    I just check and recheck my expression without those dizzying numbers.

    A bit of cheating, use Math app to calculate after assigning the value. I'm not a teacher but I guess he likes to see the working not the final answer.
     
  13. Nov 23, 2015 #12

    SteamKing

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    Whatever floats your boat.
     
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