Need Help..Prof reluctant..Math stuff..Double Integrals

[Syringer]

My Prof claims that we are not doing hw and just copying his work when we ask him questions regarding hw in class. So he is reluctant to help us on our work. So I need some help.

1. A lamina occupies the part of the disk x^2 + y ^2 <= 1 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x axis.

2. Find the center of mass of a lamina in the shape of an iosceles right triangle with equal sides of length "a" if the density at any point is proportional to the sqare of the distance from the vertex opposite the hypotenuse.


Please help. Any help is appreciated thanks! I just need someone to help me set up the equation and I can do the integrals myself. Thanks.

 

[MichaelD]

Lamina. Not to be confused with Labia. "Find the mass of the Labia at it's central point..." an interesting assignment, to be sure! It blows my mind that people can actually solve equations like this. Amazing. Awe-inspiring. I can take apart a car engine with my eyes closed and put it back together just by feeling the pieces (not quite, but darn close.....) but anything other than x + 5 = 10 and I'm lost. Sadness.

me\<---is dumbass at math

 

[Syringer]

MichaelD

Oh shoot! I sure wished you could have helped me... ANYONE know what to do?

 

[MichaelD]

I'm sorry I disappointed you! Really. OK, bump for you.

 

[Syringer]

Thanks for taking the time to read about this...hardly anyone would even bother to read it. Cudos to you!

 

[Aelus]

What's a Lamina?

it would help if you'd draw a figure of the homework and put it online somewhere

Aelus

 

[nd]

Hmm, I found these formulas in my calculator from when I took calc 3:

Mass: m = (double int) p (x,y)dA where p=density

Moment: Mx = (double int) y * p (x,y) dA

My = (double int) x * p(x,y)

Center of Mass = (My/m, Mx, m)

Maybe this helps?

 

[Syringer]

I know of the formula...I just need help setting up the problem. I dont' know what p(x,y) is. Anyways...I can't draw a picture because there ins't one in the book. And I dont' have tools to post one on a website and draw one on computer. Anyways...A lamina is just an object with density.

 

[nd]

p(x,y) is density as a function of position in the XY plane. They give you this function in the problem:



<< the density at any point is proportional to its distance from the x axis. >>

Of course, this just means p(x,y) = |y|

 

[Syringer]

Interesting....so ... anyone have any more ideassS???

 

[Syringer]

Anyone out there who can do these stuff?

 

[EHobaX]

Nope. Sorry. It's been 3 years since I've taken Calc 3, and I can honestly say I've never used the stuff since.

 

[Syringer]

That's okay...but I am stil looking for people who know how to do the 2 problems...anyone? And thanks to all those that tried