Center (in y direction) of Mass of 3D pyramid

  • #1

Homework Statement



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).

Homework Equations



ycm = (1/M) * ∫ydm, M = mass total

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.
 

Answers and Replies

  • #2
gneill
Mentor
20,925
2,867
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:
 
  • #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.
 
  • #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...

TYVM.
 

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