Density calculation sometimes can be confusing

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SUMMARY

The discussion centers on the confusion surrounding density calculations, particularly in comparing two lead cubes with different weights and areas. The first lead cube weighs 6078 grams with an area of 3376 cm, yielding a density of 1.800 g/cm², while the second weighs 5216 grams with an area of 2713 cm, resulting in a density of 1.922 g/cm². It is clarified that density is defined as mass divided by volume, not area, and that density remains constant for a material regardless of the object's size. The conversation highlights the importance of accurate terminology and understanding the distinction between mass, volume, and density.

PREREQUISITES
  • Understanding of basic physics concepts, particularly mass, volume, and density.
  • Familiarity with the formula for density: Density = Mass/Volume.
  • Knowledge of how to measure volume for geometric shapes, specifically cubes.
  • Awareness of the differences between extensive and intensive properties of matter.
NEXT STEPS
  • Research the concept of volumetric density and its applications in material science.
  • Learn about the differences between areal density and volumetric density, especially in medical imaging.
  • Explore the effects of temperature and pressure on the density of materials.
  • Study the properties of hydroxyapatite and its relevance in bone density measurements.
USEFUL FOR

This discussion is beneficial for students studying physics or chemistry, medical professionals involved in densitometry, and anyone interested in the physical properties of materials, particularly in relation to density calculations.

  • #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.
 
  • #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.
 
  • #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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