Where is the mass of the joined squares?

[Sneakatone]

I did Xcm=Lx/(xyz) Ycm=Ly/(xyz) Zcm=Lz/(xyz)

I modeled it from the equation CM=(mx+...)/M

 

[ap123]

I did Xcm=Lx/(xyz) Ycm=Ly/(xyz) Zcm=Lz/(xyz)

Is this your answer?

 

[Sneakatone]

yes that is my answer

 

[ap123]

yes that is my answer

What are x, y and z in these expressions?

 

[Sneakatone]

I believe they are axis coordinates, but cas they also be mass?

 

[ap123]

Your answer shouldn't involve these variables.
Go back a bit - can you find the centre of masses of the individual plates?

 

[Sneakatone]

L*L if your talking about one of the faces.

 

[ap123]

L*L if your talking about one of the faces.

That's not the COM of the face.

Have a look at the bottom face - since it is a uniform square, then the COM must be at its geometric centre. The same for the other 2 faces.
Then replace each of the faces by a single particle at their COM - you can then combine these to get the overall COM

 

[Sneakatone]

so would the faces turn to xy,xz,yz ?

 

[ap123]

so would the faces turn to xy,xz,yz ?

not sure what you mean?

Hint : The COM of the bottom piece is the point ( L/2, L/2, 0 )

 

[Sneakatone]

so the xz piece would be (L/2 0 L/2)
and the xy piece would be (0 L/2 L/2)

 

[ap123]

so the xz piece would be (L/2 0 L/2)
and the xy piece would be (0 L/2 L/2)

The second one here is the yz piece.

So, now just regard the mass of each piece as being concentrated at its COM and you end up with a system of 3 particles.
Then use the definition of the COM to find the overall COM of these 3 particles.

 

[Sneakatone]

will the combined mass be just L.
or will each axis (x y z) be the mass?

 

[ap123]

will the combined mass be just L.
or will each axis (x y z) be the mass?

?

Hint : in the xy plane, you can replace the piece of mass m with a particle of mass m at the point (L/2, L/2, 0).
Do the same for the other 2 pieces.

 

[Sneakatone]

xy=xL/2+yL/2+x0
xz=xL/2+y0+zL/2
yz=x0+yL/2+zL/2

 

[ap123]

xy=xL/2+yL/2+x0
xz=xL/2+y0+zL/2
yz=x0+yL/2+zL/2

I'm afraid this is not right :(
Why are you using x, y, and z?

What is the definition of centre of mass?

 

[Sneakatone]

center of mass is where the weighted position vectors to point sum is zero

 

[ap123]

So, the CM is given by

$$\mathbf r_{CM} =\frac{1}{M} \sum m_i \mathbf r_i$$

You have the position vectors r_i for each of the 3 parts. Call the mass of each piece m and then apply the above equation.