If the human body has an average density of 989 kg/m^3. what fraction of a person is submerged when floating gently in fresh water? What fraction of a person is submerged when floating gently in salt water, which has a density of 1027 kg/m^3?
When a person is floating gently in fresh water, they are displacing an amount of water equal to their weight. The fraction of the person that is submerged can be determined by comparing the density of the person to the density of fresh water.
density of person = 989 kg/m^3
density of fresh water = 1000 kg/m^3 (approximate value)
fraction submerged in fresh water = density of person / density of water
fraction submerged in fresh water = 989 kg/m^3 / 1000 kg/m^3
fraction submerged in fresh water = 0.989 or 98.9%
Therefore, approximately 98.9% of a person is submerged when floating gently in fresh water.
When floating gently in salt water, the fraction of a person that is submerged can be calculated in the same way, but using the density of salt water (1027 kg/m^3) instead.
fraction submerged in salt water = density of person / density of salt water
fraction submerged in salt water = 989 kg/m^3 / 1027 kg/m^3
fraction submerged in salt water = 0.962 or 96.2%
Therefore, approximately 96.2% of a person is submerged when floating gently in salt water.