Posted by calculs3 on Thursday, May 31, 2012 at 6:55pm.
If we are dealing with real numbers x must be >/=0 becaue y^2 may not be negative
find vertical cg
y = 2 sqrt |x|
integrate from (0,0) to (4,4)
y of cg
= int dy y (4-x) (ky) / int dy(4-x) (ky)
numerator (the moment)
4 k y^2 dy - k dy y^2 (y^2/4)
4 k y^3/3 - k y^5/20
at y = 4
85.33 k - 51.2 k = 34.1 k
denominator (the mass)
dy(4-x) (ky) = 4k y dy - k y (y^2/4)dy
= 2 k y^2 - k y^4/16
at y = 4
32 k - 16 k = 16 k
so
34.1 k / 16 k = 2.13
You can do the stripes the other way for the Xcg
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