6.22 )An ornithologist weighs a bird bone in air and in water to find the bone's density. The mass of the bone in air is 25.0 g and its apparent mass in water is 2.0 g.
a. What mass of water does the bone displace?
b. Calculate the volume of water displaced.
c. Assuming the bone's volume to be equal to that of the water displaced, calculate the density of the bone.
Note: Provide me a solution/formula pls? Thanks!
I will be happy to critique your work.
a. To find the mass of water displaced by the bone, we need to subtract the apparent mass of the bone in water from its mass in air.
Mass of water displaced = Mass of bone in air - Apparent mass of bone in water
Mass of water displaced = 25.0 g - 2.0 g
Mass of water displaced = 23.0 g
b. The volume of water displaced by the bone can be calculated using the formula:
Volume = Mass of water displaced / Density of water
The density of water is approximately 1 g/cm³.
Volume = 23.0 g / 1 g/cm³
Volume = 23.0 cm³
c. Assuming the volume of the bone is equal to that of the water displaced, we can calculate the density of the bone using the formula:
Density = Mass of bone in air / Volume
Density = 25.0 g / 23.0 cm³
Density = 1.09 g/cm³
a. To find the mass of water displaced by the bird bone, we need to use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced.
In this case, the mass of the bone in air is 25.0 g, and its apparent mass in water is 2.0 g. The apparent mass is the difference between the mass of the bone in air and the mass of the bone in water.
So, the mass of water displaced by the bone is calculated as follows:
Mass of water displaced = Mass in air - Apparent mass in water
= 25.0 g - 2.0 g
= 23.0 g
Therefore, the mass of water displaced by the bone is 23.0 g.
b. The volume of water displaced can be calculated using the formula:
Volume of water displaced = Mass of water displaced / Density of water
The density of water is typically around 1 g/cm³. So, using the mass of water displaced (23.0 g), we can calculate the volume of water displaced as follows:
Volume of water displaced = 23.0 g / 1 g/cm³
= 23.0 cm³
Therefore, the volume of water displaced by the bone is 23.0 cm³.
c. Assuming the bone's volume to be equal to that of the water displaced, we can calculate the density of the bone by dividing the mass of the bone in air by the volume of water displaced:
Density of bone = Mass of bone in air / Volume of water displaced
Using the given mass of the bone in air (25.0 g) and the calculated volume of water displaced (23.0 cm³), we can calculate the density as follows:
Density of bone = 25.0 g / 23.0 cm³
Therefore, the density of the bone is 1.08 g/cm³.