How Do You Calculate the Center of Mass of a Parabolic Plate?

[whereisccguys]

A uniform plate of height 1.59 m is cut in the form of a parabolic section. The lower boundary of the plate is defined by: y=0.65x^2. Find the distance from the rounded tip of the plate to the center of mass.

i tried to do this usin calculus and got the answer Ycm=1.01 which was wrong and used the equation given to me in class Ycm = 2/3 h which is Ycm = 1.06... which is still wrong... can someone help me?

 

[Gamma]

I am getting 3/5 h . I am sleepy. Let me know if this is correct.

 

[whereisccguys]

yea it is how'd u get that?

 

[Gamma]

Use the genaral formula for C.M.

$$\overline{x} \int dm =\int x dm$$ ------------ (1)

Choose an element of thickness dy at a distance y from the origin.

Take $$\rho$$ as the areal mass density,

Write expression for dm in terms of $$\rho$$ and y only.

Use equation (1) to find the $$\overline{x}$$