# Material engineering calculation

1. Sep 5, 2015

### Andy7199

1. The problem statement, all variables and given/known data
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.

2. Relevant 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

3. The attempt at a solution

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.

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2. Sep 5, 2015

### Staff: Mentor

I would not recommend solving a problem like this using memorized formulas. Try the following and see how it works for you.

Take as a basis 100 gm of dry bone. How many grams of apatite are there? How many grams of dry collagen are there? What is the volume of this amount of apatite? What is the volume of this amount of dry collagen? What is the total volume? What is the volume percent apatite? What is the volume percent dry collagen?

Now take as a basis 100 cc of bone in vivo. What is the volume of water? What is the volume of apatite plus dry collagen? What is the volume of apatite? What is the volume of collagen? What is the volume percent apatite? What is the volume percent of collagen?

How do these answers compare with the results you obtained with your formulas?

Chet