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The average human has a density of \(945 \mathrm{~kg} / \mathrm{m}^{3}\) after inhaling and \(1020 \mathrm{~kg} / \mathrm{m}^{3}\) 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 \(1230 \mathrm{~kg} / \mathrm{m}^{3}\) ) 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)?

Short Answer

Expert verified
After inhaling, about 23% of a human's body would be above the surface of the Dead Sea, and after exhaling, about 17% would be above the surface. 'Sinkers' are generally more muscular and have less body fat while 'floaters' have a higher fat percentage or fat distributed in a way that promotes buoyancy.

Step by step solution

01

Compute the Ratio of Body Density to Dead Sea Water Density for the Inhale Case

To calculate the proportion of the body that would be above the surface after inhaling, divide the density of the human body after inhaling (945 kg/m3) by the density of the Dead Sea water (1230 kg/m3).
02

Compute the Ratio of Body Density to Dead Sea Water Density for the Exhale Case

Similarly, to find the proportion of the body that would be above the surface after exhaling, divide the density of the human body after exhaling (1020 kg/m3) by the density of the Dead Sea water.
03

Convert the Ratios to Percentages

Multiply each ratio from Steps 1 and 2 by 100 to convert them to percentages. These percentages represent the proportion of the human body that would be submerged in the Dead Sea water; subtract each from 100% to find the percentage that would be above the surface.
04

Discuss 'Sinkers' vs 'Floaters'

'Sinkers' and 'floaters' can be differentiated by their body compositions - particularly the density and distribution of muscle and fat. Denser substances like bone and muscle sink, while less dense substances like fat float. Therefore, individuals with a higher percentage of body fat or whose fat is distributed in such a way as to optimize buoyancy (e.g., around the waist) tend to float, while 'sinkers' are generally those with more dense muscle mass and less body fat.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Density
Density is a fundamental concept in understanding buoyancy and how objects, including humans, interact with water. In simple terms, density is the mass of an object divided by its volume. It is often expressed in units like kilograms per cubic meter (kg/m³).
When we apply this to the human body and water, particularly the Dead Sea, we can start to understand why some objects float while others sink. The Dead Sea has a remarkably high density of around 1230 kg/m³ because of the high salt content, making it easier for things to float in it compared to regular water.
To determine whether a person or object will float, we compare their density to that of the surrounding water. If their density is less than the water's density, they will float. Conversely, if their density is more, they will sink. This is why, when inhaled, humans with a density of 945 kg/m³ float more easily on the Dead Sea.
Floating and sinking
The concepts of floating and sinking are key to understanding buoyancy, which is the force that allows objects to either float or sink in a fluid like water. The principle behind this is called Archimedes' principle, which states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
Whether an object floats or sinks depends on its density compared to the fluid it's in. If we take a human body as an example, when inhaling, the air in the lungs decreases the body's overall density, allowing it to displace an amount of Dead Sea water equal to its weight, thus achieving buoyancy. Conversely, when exhaling, the density increases, and the body's ability to float decreases, but in the Dead Sea's dense waters, it still remains buoyant to a large extent.
The percentage of the body above the water's surface gives an idea of how much the body is floating. After inhaling, humans have around 23% of their bodies above the surface, as calculated from the density ratios. However, this percentage decreases to approximately 17% when exhaling.
Human body composition
The human body composition plays a significant role in determining whether someone is more likely to be a "floater" or a "sinker." Body composition refers to the proportion of fat, muscle, bone, and other tissues in the body.
Fat is less dense than water, which means individuals with a higher percentage of body fat tend to float more easily. This is because fat increases buoyancy by lowering the overall body density, helping them float with a higher proportion of their body above water.
On the other hand, muscle and bone tissue are denser than water. Individuals with more muscle mass or denser bones have a tendency to sink, especially in water less dense than the Dead Sea. The distribution of body mass also affects buoyancy. When fat is distributed in areas that optimize buoyancy, such as around the waist, individuals tend to float more efficiently. This distinction between floaters and sinkers highlights how even subtle differences in body composition can influence swimming and survival in water environments.

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