Question

Bird bones have air pockets in them to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. Suppose an ornithologist weighs a bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g (assume the bone is watertight). (a) What mass of water is displaced? (b) What is the volume of the bone? (c) What is its average density?

(a) 41.4 g
(b) 12.5 cm³
(c) 3.96 g/cm³
(d) 0.00821 g/cm³

Answer 1

The mass of water displaced is 41.4 g. The volume of the bone is 45.0 cm³. The average density of the bone is 1.00 g/cm³.

Step-by-step explanation:

Given that the bone is watertight, we can use Archimedes' principle to solve this problem.

(a) The mass of water displaced is equal to the mass of the bone in air minus the apparent mass of the bone when submerged. Mass of water displaced = Mass in air - Apparent mass when submerged. Therefore, mass of water displaced = 45.0 g - 3.60 g = 41.4 g.

(b) The volume of the bone can be calculated using the formula Volume = Mass / Density. Since the mass of the bone is 45.0 g and we know the density of water is 1 g/cm³, the volume of the bone is 45.0 cm³.

(c) The average density of the bone is given by the formula Average Density = Mass / Volume. Plugging in the values, Average Density = 45.0 g / 45.0 cm³ = 1.00 g/cm³.