Density calculation sometimes can be confusing

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Discussion Overview

The discussion revolves around the calculation of density using two cubes of lead, focusing on the confusion arising from using area instead of volume in the density formula. Participants explore the implications of density as a property of materials, questioning how density relates to size and weight.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the density of two lead cubes but uses area instead of volume, leading to confusion about the relationship between size and density.
  • Several participants clarify that density is defined as mass divided by volume, not mass divided by area.
  • There is a discussion about whether the density of materials changes with size, with some asserting that density remains constant for the same material regardless of size.
  • One participant expresses confusion about the concept of density, equating it with weight or mass.
  • Another participant introduces the idea of experimental uncertainties affecting density measurements, suggesting that measurement errors could account for discrepancies in calculated densities.

Areas of Agreement / Disagreement

Participants generally agree that density is a property of the material itself and does not depend on the size of the object made from that material. However, there is some confusion regarding the definitions and implications of density, as well as the use of area versus volume in calculations.

Contextual Notes

Participants note the importance of using correct units and definitions when discussing density, highlighting that the initial confusion stemmed from using area instead of volume. There is also mention of the need for clarity regarding the source of numerical values used in examples.

  • #31
Borek said:
"weight/mass and the size", just like you stated in what I quoted.

That's how those DEXA scan machines calculated the bone mineral density. You stated previously "Bone density as measured by clinical densitometry is different from the density understand as a physical property of matter. Names are similar but they mean different things." I agree with it.
 
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  • #32
Borek said:
"weight/mass and the size", just like you stated in what I quoted.

I mean, the mass or weight and the two-dimensional surface or area which is basically two-dimensional representation of the bone size are already there before we divide them to get the surface/areal density.
 
  • #33
wonderingchicken said:
That's how those DEXA scan machines calculated the bone mineral density.

Nope. They _measure_ optical density and bone cross section (these things are doable using xray image) and _estimate_ bone mass and bone volume from these numbers. You got it reversed.
 
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  • #34
Borek said:
Nope. They _measure_ optical density and bone cross section (these things are doable using xray image) and _estimate_ bone mass and bone volume from these numbers. You got it reversed.

By dividing mass/weight with the surface/area. Correct?
 
  • #35
wonderingchicken said:
By dividing mass/weight with the surface/area. Correct?
No. You do not have the mass or weight. That is why you need to estimate it from what you can infer.
 
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  • #36
Orodruin said:
No. You do not have the mass or weight. That is why you need to estimate it from what you can infer.

So, the bone mineral weight or mass that is calculated from the DEXA scan machines are just estimations?
 
  • #37
Yes. You actually measure mass with something like a mass scale which measures force due to mass. The machine you describe can measure the attenuation of the x-ray beam as it passes through the bone and that is correlated to mass.
 
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