The average human has a density of 940 kg/m3 after inhaling and 1028 kg/m3 after exhaling.
(a) Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea (a lake with a water density of about 1230 kg/m3) in each of these cases?
(b) Given that bone and muscle are denser than fat, what physical characteristics differentiate "sinkers" (those who tend to sink in water) from "floaters" (those who readily float)?
(a) To determine the percentage of the human body above the surface in the Dead Sea, we need to compare the densities.
For the average human after inhaling:
Density of human = 940 kg/m^3
Density of water in the Dead Sea = 1230 kg/m^3
The human body will float if its density is less than that of the water. In this case, the human is less dense than the water, so it will float. However, let's calculate the percentage of the body above the surface.
Percentage above surface = (Density of water / Density of human) * 100
Percentage above surface = (1230 kg/m^3 / 940 kg/m^3) * 100
Percentage above surface ≈ 131.38%
For the average human after exhaling:
Density of human = 1028 kg/m^3
Percentage above surface = (Density of water / Density of human) * 100
Percentage above surface = (1230 kg/m^3 / 1028 kg/m^3) * 100
Percentage above surface ≈ 119.72%
(b) Sinkers and floaters are differentiated based on their relative densities. The human body's overall density depends on the composition, including bone, muscle, and fat.
Sinkers tend to have a higher overall density, meaning they are denser than the water they are submerged in. This can be due to having a higher proportion of muscle and bone, which are denser than fat. Sinkers may also have a lower body fat percentage.
Floaters, on the other hand, have a lower overall density, meaning they are less dense than the water. They may have a higher proportion of body fat, as it is less dense compared to muscle and bone.
It's important to note that individual body composition can also play a significant role in determining whether a person is a sinker or a floater.
(a) To solve this problem, we need to compare the density of the human body with the density of the water in the Dead Sea.
1. Calculate the percentage of the human body above the surface for each case by using the formula:
Percentage above surface = (Density of the human body / Density of water) * 100
For the first case, when the human body has a density of 940 kg/m3:
Percentage above surface = (940 kg/m3 / 1230 kg/m3) * 100
For the second case, when the human body has a density of 1028 kg/m3:
Percentage above surface = (1028 kg/m3 / 1230 kg/m3) * 100
2. Calculate the percentage above surface for each case by dividing the density of the human body by the density of water and multiplying by 100.
(b) The physical characteristics that differentiate "sinkers" from "floaters" are related to body composition and density distribution:
1. Fat content: Fat is less dense than muscle and bone and tends to make a person more buoyant. Higher fat content makes it easier to float, while lower fat content makes a person more likely to sink.
2. Muscle and bone density: Muscle and bone are denser than fat. People with higher muscle and bone densities tend to be more sinkers, as their overall density is higher.
3. Lung capacity: Lung capacity influences buoyancy. Those with larger lung capacity can hold more air, making them more buoyant and more likely to float.
4. Body shape: The distribution of weight and the shape of the body can affect buoyancy. People with a higher concentration of weight in their lower body area may find it easier to float, as the lower body displaces more water.
Body composition and density distribution vary from person to person, so these characteristics can determine whether someone is a sinker or a floater.
force up = force down
force up = volume in water* density of water * g
force down = weight = m g = total volume * body density * g
so for example after inhaling
force up = volume in water * 1230 * g
force down = total volume * 940* g
so
volume in water/total volume = 940/1230
multiply by 100 to get percent
Of course the less dense material floats higher, the fat person.
force down =