# Where is the mass of the joined squares?

1. Mar 29, 2013

### Sneakatone

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

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

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2. Mar 29, 2013

### ap123

3. Mar 29, 2013

### Sneakatone

4. Mar 29, 2013

### ap123

What are x, y and z in these expressions?

5. Mar 29, 2013

### Sneakatone

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

6. Mar 29, 2013

### ap123

Go back a bit - can you find the centre of masses of the individual plates?

7. Mar 29, 2013

### Sneakatone

8. Mar 29, 2013

### ap123

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

9. Mar 29, 2013

### Sneakatone

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

10. Mar 29, 2013

### ap123

not sure what you mean?

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

11. Mar 29, 2013

### Sneakatone

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

12. Mar 29, 2013

### ap123

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.

13. Mar 29, 2013

### Sneakatone

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

14. Mar 29, 2013

### ap123

?

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.

15. Mar 29, 2013

### Sneakatone

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

16. Mar 29, 2013

### ap123

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

What is the definition of centre of mass?

17. Mar 29, 2013

### Sneakatone

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

18. Mar 30, 2013

### ap123

So, the CM is given by

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

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