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Center of mass of two metal solids.

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Figure 7-29 shows a composite slab with dimensions 22.0 cm multiplied by 13.0 cm multiplied by 2.8 cm. Half of the slab is made of aluminum (density = 2.70 g/cm3) and half of iron (density = 7.85 g/cm3), as shown. How far from the line joining the two metals is the center of mass of the slab



    09_31.gif


    2. Relevant equations

    Center of mass equations: ([tex]\Sigma[/tex]X*r)/M

    M = total mass

    3. The attempt at a solution

    So, since there are two slabs of metal connected to each other, I first found the center of mass of each metal and then found the center of mass of both together.

    Using common sense and the assumption that the density is uniform, the center of masses for each block would be in the exact middle of the metals.

    I made my origin for the coordinate system at the bottom left vertex of the the iron part of the slab, where x=0, y=0, and z=0.

    For iron, I obtained the (x,y,z) coordinates of (5.5, 6.5, 1.4)

    and aluminum (x,y,z) coordinates of (16.5, 6.5, 1.4)

    now, I want to find r[tex]_{}cm[/tex], which i did by squaring all the values, added them together, and the found the square root of that sum:

    Iron: r[tex]_{}cm[/tex]: 8.62902
    Aluminum: r[tex]_{}cm[/tex]: 17.7893

    I found the mass by finding half the volume of the slab, and multiplying each density by half that volume.

    so, no i use the center of mass equation, ([tex]\Sigma[/tex]X*r)/M, and get a value of 10.9734 centimeters

    Now, to find how far it is from the line, I made a triangle, where 11-10.9734 and 1.4 are my legs, and the hypotenuse is the distance. Using the theorem, i get an answer of:

    1.40025 centimeters

    Answer does not seem right, so I'm wondering what I might have done wrong?
     

    Attached Files:

  2. jcsd
  3. Oct 14, 2009 #2

    Delphi51

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    Homework Helper

    The y and z parts are obvious, so just do the x:
    sum of (m*r)/(sum of masses)
    x = (massOfIron*5.5 + massOfAl*16.5)/(total mass)
     
  4. Oct 14, 2009 #3
    Why are the y and z parts obvious?
     
  5. Oct 14, 2009 #4
    Nevermind i got it. Thanks for your help!!!!
     
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