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 43.0 g and its apparent mass when submerged is 3.60 g (the bone is watertight).

What mass of water is displaced?

What is the volume of the bone?

What is its average density?

1.0

To find the mass of water displaced by the bird bone, we can use Archimedes' principle, which states that the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object.

First, we need to find the weight of the water displaced. The weight of the water is given by the equation:

Weight of water = Mass of water × acceleration due to gravity

In this case, the acceleration due to gravity is approximately 9.8 m/s^2.

Using the apparent mass when submerged (3.60 g), we can find the weight of the water displaced:

Weight of water = 3.60 g × 9.8 m/s^2

Next, we find the volume of water displaced. Since the density of water is 1 g/cm^3, the volume of water displaced is equal to its mass:

Volume of water = 3.60 g

To find the volume of the bone, we can use the fact that the density of an object is defined as its mass divided by its volume:

Density = Mass / Volume

From the given data, we know the mass of the bone is 43.0 g. Substituting the values, we can rearrange the equation to solve for volume:

Volume of the bone = Mass of the bone / Density of the bone

The average density of the bone is its density in air, as it is a watertight bone given in the problem.

Finally, to find the average density of the bone, we can divide its mass (43.0 g) by its volume.