Hi im new so maybe one of you can help me understand this question, can't find it anywhere in the book.
A person weighs 723N in air and has a body-fat percentage of 29.3% .
What is the overall density of this person's body?
What is the volume of this person's body?
Find the apparent weight of this person when completely submerged in water?
So very confused
There are two formulas used for calculating body-fat (fraction) from density:
Brozek formula: BF =(4.57/ρ-4.142)
Siri formula is: BF = (4.95/ρ−4.50)
Take the inverse of the first one:
F=BF(ρ)=(4.57/ρ-4.142)
R1(F)=ρ=4.57/(F+4.142)
or the Siri formula:
F=BF(ρ)=(4.95/ρ-4.5)
R2(F)=ρ=4.95/(F+4.5)
For F=29.3%=0.293,
R1(F)=1.030
R2(F)=1.0327
Use the average of 1.031
Mass = 723N/9.8
=73.8 kg
Volume = mass/density
=73.8/1031 kg/m³
=0.072 m³
Apparent weight in water and neglecting density of air
= 73.8*(1.031-1)= 2.3 kg.
No problem, I can help you understand how to approach these questions step by step.
To find the overall density of a person's body, you need to use the formula:
Density = Mass / Volume
However, in this case, the mass is not given directly. We are only given the weight of the person. To find the mass, you can divide the weight by the acceleration due to gravity (g).
Step 1: Find the mass of the person
Weight = Mass * g
Mass = Weight / g
You are given that the person's weight in air is 723N. To find the mass, you need to know the value of g, which is approximately 9.8 m/s^2.
Mass = 723N / 9.8 m/s^2
Now that you have the mass, you can proceed to find the volume of the person's body.
Step 2: Find the volume of the person's body
To find the volume, you can use the formula:
Density = Mass / Volume
In this case, the density is not given, so you need to rearrange the formula to solve for volume:
Volume = Mass / Density
However, we still don't have the density of the person's body directly. We are given the body-fat percentage, which can help us estimate the density.
Step 3: Estimate the density of the person's body
The density of body fat is lower than the density of lean body mass. To estimate the density of the person's body, we can assume that the person's body is made up of two components: body fat and lean body mass.
The overall density (ρ) of the person's body can be calculated using the following formula:
ρ = ρ_fat * (fat_percentage / 100) + ρ_lean * (1 - fat_percentage / 100)
In this formula, ρ_fat is the density of body fat, ρ_lean is the density of lean body mass, and fat_percentage is the given body-fat percentage, which is 29.3%.
The density of body fat is approximately 0.9 g/cm^3, and the density of lean body mass is approximately 1.1 g/cm^3.
Now that we have the density, we can calculate the volume of the person's body using the formula:
Volume = Mass / Density
Step 4: Find the apparent weight when completely submerged in water
When a person is submerged in water, the apparent weight is equal to the weight of the water displaced by the person's body. In other words, it is equal to the weight of the volume of water that is displaced.
To find the apparent weight, we can use the formula:
Apparent Weight = Weight - Buoyant Force
The buoyant force can be calculated using the formula:
Buoyant Force = Density of Water * Volume * g
In this formula, the density of water is approximately 1000 kg/m^3, Volume is the calculated volume of the person's body, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
I hope this step-by-step explanation helps you approach these questions!