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Homework Help: Center of Mass and Mass

  1. Sep 18, 2016 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    triple integrals, center of mass

    3. The attempt at a solution
    I set up the triple integral

    x: lower limit 0 upper limit 1
    y: lower limit 0 upper limit 2
    z: lower limit 0 upper limit 1

    ∫∫∫ δ(x,y,z) dx dy dz
    => applied the limits for x, y and z, and δ(x,y,z) = 2 +xy -2z (given)

    I got mass is equal to 1.

    Then I tiried to find x bar (x coordinate of center of mass)
    set up this way: ∫∫∫ (x * δ(x,y,z) dx) dz dy divide by Mass (Mass = 1 from previous result)

    and got x bar = 1.667, which does not make sense, cuz 0≤ x ≤1 how come it is outside the x limits, or what was the mistake?
  2. jcsd
  3. Sep 18, 2016 #2


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    How are we to know what your mistake is without you showing us your work? Probably a mistake in algebra or integration.
  4. Sep 18, 2016 #3


    Staff: Mentor

    Here's your integral, formatted using LaTeX. Click on it to see what I wrote.
    $$\int_{z = 0}^1 \int_{y = 0}^2 \int_{x = 0}^1 2 + xy - 2z \ dx \ dy \ dz$$
  5. Sep 18, 2016 #4
  6. Sep 18, 2016 #5


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  7. Sep 19, 2016 #6


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    It is wrong. Check your work.
  8. Sep 20, 2016 #7
    Realized the problem, should be 3, algebraic mistake :P
  9. Sep 20, 2016 #8
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