Where is the center of mass of the slab

[ganondorf29]

Homework Statement

The figure shows the dimensions of a composite slab; a fraction of the slab is made of aluminum (density = 2.70 g/cm3) and other part is made of iron (density = 7.85 g/cm3). They are not equal as indicated in the figure, but have x1 = 7.5 cm and x2 = 14.5 cm. As measured from the interface b etween the two metals, where is the center of mass of the slab ( cm)? (Take + toward aluminum with the origin as the midpoint.)

Homework Equations

density = m/v
xcom = (m1x1 + m2x2)/M

The Attempt at a Solution

I found the volumes and then the mass of each section. I got the mass of the Iron slab to be 2143g and the mass of the Aluminum slab to 1425.6g. I assumed that the center of mass for each slab would be the middle if it was not connected to the other slab. So I got the center of mass for the Iron slab to be (3.75,6.5) and the Aluminum slab to be (7.25,6.5). Then I used xcom = (m1x1 + m2x2)/M and got around 5.15 cm. That doesn't seem right. Any suggestions?

 

[JoAuSc]

That isn't right. Relative to the boundary, x1 is negative.

 

[krausr79]

Call the left-hand side the origin, and the centers will be 3.75 (iron) and 14.75(aluminium). Calculate the center from there. I wasn't quite sure whether you meant for the interface (at 7.5) to be the origin or the midpoint (at 11), so once you have the left-origin center, subtract either 7.5 or 11 from that depending on which you want.