# Material science calculation

1. Sep 4, 2015

### Andy7199

Hi everyone, I know this is a standard textbook question but I am really wondering whether I am wrong or not.
My solution is shown as below but can anybody please give me some opinion? Cause I think it is too simple for this question...Thank you so much.

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.

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)
vf = 48.3 %

Volume percentages of collagens:
vf = (30/1.2) / (70/3 + 30/1.2)
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 %

2. Sep 9, 2015