Center of mass of two connected different density blocks

AI Thread Summary
The discussion revolves around calculating the center of mass (COM) of a composite slab made of aluminum and iron with different densities. Participants suggest that the problem can be simplified by calculating the mass and COM of each block separately before determining the overall COM. There is confusion regarding the vertical x-coordinate, with some asserting it should be 6.7 cm based on symmetry, while others suggest it may need to be adjusted to -6.7 cm due to its position on the negative side of the axis. The importance of considering the density ratio between the two materials is emphasized for accurate calculations. Overall, the conversation highlights the methodical approach to finding the COM while addressing specific points of confusion.
J-dizzal
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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


20150707_161138_zpsvokykdw2.jpg


The Attempt at a Solution


I thought i applied the formulas correctly
20150707_161132_zpsa7yycxn5.jpg
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Its easier without calculus. Compute the mass and center of the two separate pieces, then compute the net CM.
 
Dr. Courtney said:
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.
 
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.
 
J-dizzal said:
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?
 
Nathanael said:
It should be.
yea, I've done it by symmetry and using the xcom formula and each time 6.7cm
 
Nathanael said:
It should be. The answer says it's not?
20150707_172625_zpsy7gbuml4.jpg
 
Perhaps it's because it lies on the negative side of the axis. Try -6.7 cm
 
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Nathanael said:
Perhaps it's because it lies on the negative side of the axis. Try -6.7 cm
yep that's why thanks sir.
 

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