Center of Mass and Mass

  • Thread starter nysnacc
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  • #1
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Homework Statement


upload_2016-9-18_10-53-47.png


Homework Equations


triple integrals, center of mass

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?
 

Answers and Replies

  • #2
LCKurtz
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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.
 
  • #3
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Here's your integral, formatted using LaTeX. Click on it to see what I wrote.
$$\int_{z = 0}^1 \int_{y = 0}^2 \int_{x = 0}^1 2 + xy - 2z \ dx \ dy \ dz$$
 
  • #6
ehild
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∫∫∫ 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.
It is wrong. Check your work.
 
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Likes nysnacc
  • #7
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It is wrong. Check your work.
Realized the problem, should be 3, algebraic mistake :P
 
  • #8
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Thanks
 

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