Centroid of an Area - Finding X & Y Coordinates

[werson tan]

Homework Statement

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)

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

total area = (75x175) +(100x175) +(0.5x50x175) -(π/4 x100x100) = 27964

You have a mistake here. The triangle has dimensions of base = 150 x height = 75

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

You have the correct dimensions of the triangle here and the correct moment arm, but you are dividing by the incorrect area.

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 ?

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.

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)

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

 

[werson tan]

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

My ans is x = 108.3 , y = 61.3 after changing 50 to 150, is my ans wrong?

 

[SteamKing]

My ans is x = 108.3 , y = 61.3 after changing 50 to 150, is my ans wrong?

It's not clear. Why don't you post your revised calculations?

 

[werson tan]

It's not clear. Why don't you post your revised calculations?

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

 

[SteamKing]

total area = (75x175) +(100x175) +(0.5x50x75) -(π/4 x100x100) = 35464

You have the wrong dimensions for the end triangle here. It is L = 150 mm, H = 75 mm

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

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.

my centroid for x = (75x175)(37.5) +(100x175) (125) + (0.5x50x175)(225)-(π/4 x100x100)(175 - (4(100)/3π) ) / 35464 = 108.3

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.

 

[werson tan]

(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..

 

[SteamKing]

(75x175) +(100x175) +(0.5x150x75) -(π/4 x100x100) = 35464

This calculation is still incorrect. Did you even bother to check the arithmetic after changing the dimensions of the triangle?

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

The centroidal locations will not be correct until you calculate the correct area for the figure. Get the first step right.

 

[azizlwl]

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.

 

[SteamKing]

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.

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?

 

[azizlwl]

I guess this is easy for me to see.
ae(a/2) + be(b/2+a) + cd/2(c/3+a+b)-πr^2//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.

 

[SteamKing]

I guess this is easy for me to see.
ae(a/2) + be(b/2+a) + cd/2(c/3+a+b)-πr^2//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.

Whatever floats your boat.