How Do You Calculate the Center of Mass of a Composite Slab?

[ticklemepink20]

1. A composite slab has dimensions of d1=11.0cm, d2=2.80cm, and d3=13.0cm. Half the slab consists of aluminum (density=2.70g/cm^3) and half consists of iron (density=7.85g/cm^3). What are the x coordinate, y coordinate, and z coordinate of the slab's center of mass?

There's a figure in my book where the dimensions are for each the iron and aluminum. In other words, if you find the volume using the dimensions they give you, if you double it you have the volume for the whole figure.


I have no idea where to even begin.
I found the volume for each piece to be 400.4g

I tried finding the mass for each using p=m/v.
For the aluminum I got m=(400.4cm^3)(2.70g/cm^3) = 1081.08g
For the iron I got m=(400.4cm^3)(7.85g/cm^3) = 3143.17g


No clue how to find x, y, and z...help please!

 

[OlderDan]

If you are saying that each metal is a rectangle 11cm x 13cm with a thickness of 2.8cm stacked to make a total thickness of 5.6cm, then by symmetry the CM position is on a line through the centers of the big ractangular faces. You just need to find the position along the direction of the 5.6cm thickness. You can do that by using the mass and the CM positions of the individual metals.