# Center of mass of two connected different density blocks

1. Jul 7, 2015

### J-dizzal

1. The problem statement, all variables and given/known data
The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 2.85 cm, and d3 = 13.4 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and(c) the z coordinate of the slab's center of mass?

http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c09/fig09_40.gif

2. Relevant equations

3. The attempt at a solution
I thought i applied the formulas correctly

2. Jul 7, 2015

### Dr. Courtney

Its easier without calculus. Compute the mass and center of the two separate pieces, then compute the net CM.

3. Jul 7, 2015

### J-dizzal

I dont see why the com in the vertical (x-axis) is not 13.4/2 = 6.7cm.

4. Jul 7, 2015

### vanoccupanther

I would approach this by getting the COM for each of the metal blocks. You then look at the different mass density ratio's of the two blocks. In the case above iron to aluminium is pretty much a 3:1 ratio. You then take the block as a whole and get the COM if both sides were the same density. Then use the COM for both blocks and adjust it with respect to the COM of the separate Fe and Al blocks in the 3:1 ratio.

For example the x direction, the COM of Fe is halfway through the block at 5.8cm, and the same for Al. Since Fe is 3 times denser than Al move the COM for both blocks closer to the COM of the Fe in a 3:1 ratio. So the overall COM in the x direction is 2.9cm from the COM of the Fe block.

Repeat that train of thought for y and z and then get the point that is closest to all three.

Sorry if that answer seems convoluted.

5. Jul 7, 2015

### Nathanael

It should be. The answer says it's not?

6. Jul 7, 2015

### J-dizzal

yea, ive done it by symmetry and using the xcom formula and each time 6.7cm

7. Jul 7, 2015

8. Jul 7, 2015

### Nathanael

Perhaps it's because it lies on the negative side of the axis. Try -6.7 cm

9. Jul 7, 2015

### J-dizzal

yep thats why thanks sir.