Question

In: Physics

For an average human, the actual values of the densities of the fat and lean tissues...

For an average human, the actual values of the densities of the fat and lean tissues are ρf = 0.9 g/cm3, and ρl = 1.1 g/cm3 respectively (fat tissue =ρf and lean tissue =ρl). Given these values, are there limitations on the body fat percentage of a human that can be suspended in a body of water? Explain your thoughts and calculate the limits if any.

HINT:

  • What are the maximum and minimum possible densities of a human? Is it possible for objects with each of these densities to be suspended in (as opposed to floating on top of) water?

PLEASE PROVIDE AN EXPLANATION

Solutions

Expert Solution

For a human to be suspended in water, their density has to be exactly .

Let the fat tissue percentage be and let the lean tissue percentage by .

A percentage implies that it is out of every parts

Therefore, we can say that for every parts, parts are fat tissue and parts are lean tissue.

Therefore,

As mentioned previously, the average density of the hundred parts needs to be .

Therefore, we have

or

Now, we have two equations and two variables.

Solving these equations for ,

or

At a fifty percent fatty tissue, the body will float.

genius_generous answered 6 months ago
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