A person weighs 872 N in air and has a body fat percentage of 20.7%.
a. What is the overall density of this person's body?
b. What is the volume of this person's body?
c. Find the apparent weight of this person when completely submerged in water.
a. The overall density of this person's body is 1.068 g/cm^3.
b. The volume of this person's body is 817.6 cm^3.
c. The apparent weight of this person when completely submerged in water is 745.2 N.
a. To find the overall density of the person's body, we need to know both the person's weight in air and their volume. Since we know the weight in air, we can calculate the weight of the person's body fat.
Weight of body fat = body weight in air x body fat percentage
Weight of body fat = 872 N x 0.207
Weight of body fat = 180.504 N
Now we can calculate the weight of the person's lean body mass (or non-fat weight) by subtracting the weight of the body fat from the weight in air.
Weight of lean body mass = body weight in air - weight of body fat
Weight of lean body mass = 872 N - 180.504 N
Weight of lean body mass = 691.496 N
The overall density of the person's body is then calculated by dividing the weight of the lean body mass by the volume of the body.
Overall density = weight of lean body mass / volume of the body
b. To find the volume of the person's body, we can use the density equation:
Density = mass / volume
Rearranging the equation, we can solve for volume:
Volume = mass / density
The mass we need is the weight of the lean body mass, which we already calculated to be 691.496 N. And the density is what we need to solve for.
Plugging in these values, we get:
Volume = 691.496 N / overall density
c. To find the apparent weight of the person when completely submerged in water, we need to consider the buoyant force exerted by the water on the person's body.
Buoyant force = weight of the displaced water
Since the volume of the person's body is the same as the volume of water displaced, we can use the volume we calculated above.
Buoyant force = density of water x volume of body x acceleration due to gravity
The apparent weight of the person when completely submerged in water is then calculated by subtracting the buoyant force from the weight in air.
Apparent weight = weight in air - buoyant force
Now, plug in the values we calculated:
Apparent weight = 872 N - (density of water x volume x acceleration due to gravity)
To answer these questions, we need to use the concept of buoyancy and Archimedes' principle.
a. The overall density of a person's body can be determined by calculating the ratio of their weight in air to the volume of their body. The formula for density is:
Density = Mass / Volume
However, we need to convert the weight to mass using the formula:
Weight = Mass x Gravity
Given that the weight of the person is 872 N, and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation:
872 N = Mass x 9.8 m/s^2
Solving for mass:
Mass = 872 N / 9.8 m/s^2
Now, we can calculate the overall density:
Overall Density = Mass / Volume
b. To find the volume of the person's body, we can use Archimedes' principle, which states that the upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The formula for volume is:
Volume = Mass / Density
Using the mass we calculated in question a and assuming an average density of a human body of 1000 kg/m^3, we can calculate the volume.
c. To find the apparent weight of the person when completely submerged in water, we need to consider the buoyant force acting on the person.
The formula for the apparent weight is:
Apparent Weight = Weight - Buoyant Force
The buoyant force can be calculated using Archimedes' principle:
Buoyant Force = Density of Water x Volume of Displaced Water x Gravity
The density of water is approximately 1000 kg/m^3, and the volume of displaced water is the same as the volume of the person's body calculated in question b.
Using the given weight and the calculated buoyant force, we can find the apparent weight.