Center of mass of two connected different density blocks

[J-dizzal]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I thought i applied the formulas correctly

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[Dr. Courtney]

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

 

[J-dizzal]

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

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

 

[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.

 

[Nathanael]

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

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

 

[J-dizzal]

It should be.

yea, I've done it by symmetry and using the xcom formula and each time 6.7cm

 

[J-dizzal]

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

 

[Nathanael]

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

 

[J-dizzal]

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

yep that's why thanks sir.