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Andy7199
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Homework Statement
Water corresponds to approximately 20 vol.% of the bone in mammals. On a dry weight basis, approximately 70 wt.% of the bone is composed of carbonated apatite. The density of apatite is ~3.0 g/cm3. Density of dry collagens is ~ 1.2 g/cm3. Calculate the volume percentages of apatite and collagen in dry bone. Calculate the volume percentages of water, apatite and collagen in bone in vivo.
Homework Equations
Vf = (Wf / ρf) / (Wf / ρf + Wm / ρm)
where Vf = Volume fraction, Wf = Weight fraction of filler, Wm = Weight fraction of maxtrix, ρm and ρf = Density of matrix and fiber respectively
The Attempt at a Solution
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Regarding the dry bone, it contains 70 wt.% of carbonated apatite and 30 wt% of collagens.
Volume percentages of carbonated apatite:
vf = [(70/3) / (70/3 + 30/1.2)] *100
vf = 48.3 %
Volume percentages of collagens:
vf = [(30/1.2) / (70/3 + 30/1.2)]*100
vf = 51.7 %
Regarding the bone in vivo, it contains 20 vol.% of water and 80 vol% of carbonated apatite and collagens.
Volume percentages of carbonated apatite:
vf = 48.3*0.8 = 38.6 %
Volume percentages of collagens:
vf = 51.7*0.8 = 41.4 %
I know this is a standard textbook question but I am really wondering whether I am wrong or not.
Can anybody please give me some opinion? Cause I think it is too simple for this question...Thank you so much.