The mass of a piece of cork is 20g. What fraction of the cork is immersed when it floats in water?
Take denisty of cork to be 0.25g/cm^3
To find the fraction of the cork that is immersed when it floats in water, we need to compare the density of the cork to the density of water.
Density = Mass / Volume
Since the mass of the cork is given as 20g and the density of cork is given as 0.25g/cm^3, we can find the volume of the cork:
Volume = Mass / Density = 20g / 0.25g/cm^3 = 80 cm^3
Next, we need to find the density of water. The density of water is approximately 1g/cm^3.
To find the fraction of the cork that is immersed, we need to compare the volume of the cork that is submerged in water to the total volume of the cork.
When the cork floats in water, it displaces an amount of water equal to its own weight. So, the volume of water displaced is equal to the volume of the cork.
The volume of the cork that is submerged can be found using Archimedes' principle:
Volume submerged = Volume of water displaced = Volume of cork = 80 cm^3
The total volume of the cork is 80 cm^3, and the volume submerged is also 80 cm^3. Therefore, the fraction of the cork that is immersed is:
Fraction immersed = Volume submerged / Total volume = 80 cm^3 / 80 cm^3 = 1
So, when the cork floats in water, the entire cork is immersed.
To find the fraction of the cork that is immersed when it floats in water, we need to compare the density of the cork to the density of water. The fraction of the cork that is immersed can be determined by the ratio of the density of the cork to the density of water.
Given:
- Mass of the cork = 20g
- Density of cork = 0.25g/cm^3
Density is defined as mass divided by volume, so we can rearrange the formula to find the volume:
Volume of the cork = Mass of the cork / Density of the cork
Volume of the cork = 20g / 0.25g/cm^3
= 80 cm^3
Now, let's assume the whole volume of the cork is V. The volume of the immersed part of the cork can be denoted as Vi, and the volume of the part above the water as Vw.
Since cork floats in water, the weight of the cork is equal to the weight of the water it displaces.
The weight of the cork = the weight of the water displaced
Mass of the cork * acceleration due to gravity = Density of water * Volume of the submerged part of the cork * acceleration due to gravity
Mass of the cork = Density of water * Volume of the submerged part of the cork
Density of cork * Volume of cork = Density of water * Volume of the submerged part
Solving for the fraction of the cork that is immersed:
Fraction of the submerged part of the cork = Volume of the submerged part of the cork / Volume of the cork
Fraction of the submerged part of the cork = Vi / V
Fraction of the submerged part of the cork = Vi / (Vi + Vw)
Since Vi is the volume of the submerged part and Vw is the volume of the part above the water,
Fraction of the submerged part of the cork = Vi / (Vi + Vw) = Vi / V
Now, let's substitute the values:
Fraction of the submerged part of the cork = Vi / V = Vi / (Vi + Vw) = Vi / 80cm^3
Hence, we cannot determine the exact fraction of the cork that is immersed with the given information. We need to know the volume of the submerged part (Vi) or the volume of the part above the water (Vw) to calculate the exact fraction.