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Homework Help: Center (in y direction) of Mass of 3D pyramid

  1. Nov 6, 2013 #1
    1. The problem statement, all variables and given/known data

    A monument is made from stone blocks of density 3800kg/m^3. The monument is 15.7m high, 64.8m wide at the base, and 3.6m thick from front th back. How much work was required to build the monument? (Hint: find ycm).

    2. Relevant equations

    ycm = (1/M) * ∫ydm, M = mass total

    3. The attempt at a solution

    Take a cross section and get a rectangle.
    The length will be: (64.8/15.7) * y
    The width will be: (3.6/15.7) * y

    Thus, dm = density * length * width * dy

    M total = density * volume = 6958742.8

    ycm = (1/M) * ∫y * density * length * width * dy (from 0 to 15.7)

    Okay, so this solution is wrong. It gives the the ycm as 7.85m. But ycm is actually a third of the height (as it is for triangles).

    My question is: what is fundamentally wrong with my approach?

    I have the solution though. I don't need that.
  2. jcsd
  3. Nov 6, 2013 #2


    User Avatar

    Staff: Mentor

    Your formulas for the length and width have them both zero for y = 0. Unless the monument is supposed to be standing on its head, that could be problematical :smile:
  4. Nov 6, 2013 #3
    That shouldn't matter.

    Take the center of mass from 7.85m from the top.

    Interestingly. 7.85m is the middle of the triangle.
  5. Nov 6, 2013 #4
    Got it got it got it! 3.6 is constant. Brb

    [EDIT] Works. You made me think of it. I was looking at integrating from the top and wrote out eqn to reverse and realized... wait a minute, i'm scaling the width but its constant...

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