Question

i have a question that i need help solving. Its moments and centers of mass. The question states that the region bounded by the parabola y=x^2 and the line y=4

Answer 1

find the center of mass of a thin plate of constant density and covering given the region and its thin plates with constant density

Answer 2

have you started working on this?

Answer 3

yes trying to i kno that bar x =0 and bar y =12/5, but i cant find the bar y

Answer 4

nvm got it

Answer 5

nice :)

Answer 6

nvm need help

Answer 7

http://math.stackexchange.com/questions/250678/how-to-find-the-center-of-mass-of-a-plane-region

Answer 8

and in order to find bar y, i have to to find Mx, which to find bar y, you have to do Mx/m which m =-4/3

Answer 9

@mrGrimm

Answer 10

@mrGrimm

This is how you can set up the double integral.
The area A is obtained by \(\int\int dx~dy \) over the region.
Mx is obtained by \(\int\int ~y~ dx~dy \) over the region.
The limits have been shown in the above figure, namely
first integrate along x, which means that the limits must be expressed in term of y, giving [-sqrt(y), +sqrt(y)]. The second integrate is along y, so [0,4].
Finally, \(\bar{y}\) = \(\dfrac{M_x}{A}\), as you probably know already.
12/5 is the correct answer, as you stated.