Posted by **calculs3** on Thursday, May 31, 2012 at 6:55pm.

Find the center of gravity enclosed by y^2=4x,x=4,y=0 if its density is given by ä(x.y)=ky

- calculus -
**Damon**, Thursday, May 31, 2012 at 7:32pm
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

## Answer This Question

## Related Questions

- physics - Find the x- and y-coordinates of the center of gravity of a 4.00 ft by...
- physics - Find the x- and y-coordinates of the center of gravity of a 4.00 ft by...
- physics - Find the x- and y-coordinates of the center of gravity of a 4.00 ft by...
- Physics - Find the x- and y-coordinates of the center of gravity of a 4.00 ft ...
- Physics - Update: Planets are not uniform inside. Normally, they are densest at ...
- Calculus - find the region enclosed by the given curves: 4x+y^2=9, x=2y
- Calculus - Find the area of the region enclosed by the given curves: 4x+y^2=9, x...
- Calculus - Find the area of the region enclosed by the given curves: y=e^6x, y=...
- calculus - Find the total area enclosed by the functions given below. y=x^2+2x+1...
- Physics ( using earth to find pressure of planet y - 3. A model of Earth’s ...

More Related Questions