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 47 g and its apparent mass when submerged is 3.4 g (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?

Answer 1

The mass of water displaced by the bird bone is 43.6 g, which also represents its volume in cubic centimeters, since 1 cm³ of water equals 1 g. The average density of the bone is found by dividing mass by volume, resulting in a density of 1.0775 g/cm³.

Step-by-step explanation:

The student's question revolves around the principles of buoyancy and Archimedes' principle. When a bird bone is submerged in water, it displaces water equal to its volume, resulting in an apparent loss of mass. This is due to the buoyant force acting opposite to gravity. For the bird bone with a mass of 47 g and an apparent submerged mass of 3.4 g:

• (a) Mass of water displaced: The mass of water displaced is equal to the difference between the mass in air and the apparent mass in water, which is 47 g - 3.4 g = 43.6 g.
• (b) Volume of the bone: Since 1 cm³ of water has a mass of 1 g, the volume of the bone that displaced water is 43.6 cm³.
• (c) Average density of the bone: The average density is mass divided by volume: 47 g / 43.6 cm³ = 1.0775 g/cm³.

Answer 2

a) 43.6g b)0.0000436m^3( 43.6cm^3) c)1078kg/m^3

Step-by-step explanation:

Mass of the bone in air = 47g = 47/1000= 0.047kg

Apparent mass of the bone in water = 3.4g

Mass of water displaced = 47g - 3.4g, from upthrust which is the upward force acting upward on the body.

Mass of water displaced = 43.6g

Volume of the bone = volume of the water displaced

Density of water (1000kg/m^3) = mass of water displaced/ volume of water

Volume of water displaced = mass of water displaced/ density = 0.0436 in kg/1000 = 0.0000436m^3 ( 43.6cm^3)

Average density of the bone = total mass/ total volume = 0.047kg/ 0.0000436m^3 = 1078kg/m^3