Centroid based on Y-coordinates

[kris8888]

Hi Everyone,

I'm trying to calculate centroid of box in attached picture. But the results are always a bit off, and I can't figure out what I'm doing wrong. Maybe I should be using Vectors but I am not very experienced in this

I know these info:

Y coordinate of A (0)
XY coordinate on line d called E (0 , 3.33)
Y coordinate on line d called F (6.66)
The space between E and F on x-axis (5)
lenght of a (7.07)
lenght of d (18.03)


See attached image for concrete example


[MATH]M = \dfrac{6.66 - 3.33}{5} = \dfrac{333}{500}[/MATH]
E = Centroid
[MATH]|AE| = \sqrt{(0.5 * 7.07)^2 + (0.5 * 18.03)^2} = \dfrac{\sqrt{3750658}}{200}[/MATH]
θ = angle between line AD and X-axis
[MATH]\tan(\theta) = \tan(M) = \tan(\dfrac{333}{500}) = 33.6636[/MATH]
ϕ = the angle between line AD and diagonal AC
[MATH]\tan(\phi) = \tan(a/b) = \tan(7.07/18.03) = 21.4113[/MATH]

[MATH]\tan(\theta + \phi) = \tan(33.6636 + 21.4113) = 55.0349 [/MATH]

[MATH]x coordinate A = \dfrac{0 - 3.33}{\dfrac{333}{500}} = -5 [/MATH]

[MATH]Centroid_x = x coordinate A + AE * \cos(\theta + \phi) = -5 + \dfrac{\sqrt{3750658}}{200} * \cos(55.0349) = 0.549285[/MATH]

[MATH]Centroid_y = y coordinate A + AE * \sin(\theta + \phi) = 0 + \dfrac{\sqrt{3750658}}{200}* \sin(55.0349) = 7.93 [/MATH]

This should have been (0 , 7.5) - what am I doing wrong ... any help would be greatly appreciated

 

[kris8888]

SOLVED

Can I delete POST

 

[MarkFL]

SOLVED

Can I delete POST

Why not post your solution instead? Others facing a similar question may find your solution useful.

 

[Dr.Peterson]

There are a few misstatements (typos?) in your work, which make it hard to follow. For one, you seem to be using E for both the point shown and the centroid; for another, you wrote [MATH]\tan(M)[/MATH] where you meant [MATH]\tan^{-1}(M)[/MATH], and similarly elsewhere.

But the biggest error I see is that in calculating |AE|, you assumed the figure is a rectangle, which it isn't. Is that what you fixed? I didn't check the details beyond these points.

 

[kris8888]

But the biggest error...