1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Center of mass of two connected different density blocks

  1. Jul 7, 2015 #1
    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?


    2. Relevant equations

    3. The attempt at a solution
    I thought i applied the formulas correctly
  2. jcsd
  3. Jul 7, 2015 #2
    Its easier without calculus. Compute the mass and center of the two separate pieces, then compute the net CM.
  4. Jul 7, 2015 #3
    I dont see why the com in the vertical (x-axis) is not 13.4/2 = 6.7cm.
  5. Jul 7, 2015 #4
    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.
  6. Jul 7, 2015 #5


    User Avatar
    Homework Helper

    It should be. The answer says it's not?
  7. Jul 7, 2015 #6
    yea, ive done it by symmetry and using the xcom formula and each time 6.7cm
  8. Jul 7, 2015 #7
  9. Jul 7, 2015 #8


    User Avatar
    Homework Helper

    Perhaps it's because it lies on the negative side of the axis. Try -6.7 cm
  10. Jul 7, 2015 #9
    yep thats why thanks sir.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted