Passage
Hydrostatic weighing is a technique used to determine an individual's overall body density. The weight of the individual is measured when their body is completely submerged in water. Because the volume of air in the respiratory system affects the measured underwater weight, the individual must exhale completely before entering the water. However, residual volume, the volume of air that always remains in the respiratory system, must also be accounted for.By comparing an individual's in-air weight to their underwater weight, their total body volume can be determined. The density of the body D_b excluding any air in the respiratory system is calculated with the in-air mass of the individual m_air, the individual's total body volume V_total, and an estimate of residual volume V_res by:
Db=mairVtotal-VresEquation 1Body density can be used to calculate an individual's body fat composition, the percentage of total body mass that is made up of fatty tissue. Human fatty tissue has an average density of 0.9 kg/L, and the density of water is 1 kg/L. The acceleration due to gravity is 10 m/s².
Adapted from Siri, WE, Body composition from fluids spaces and density. Nutrition 1956 Springer Nature.
-A 0.3-kg object with half the density of human fatty tissue is placed in water. Ignoring the atmospheric pressure, what percentage of the mass will be submerged?

Question

Passage
Hydrostatic weighing is a technique used to determine an individual's overall body density. The weight of the individual is measured when their body is completely submerged in water. Because the volume of air in the respiratory system affects the measured underwater weight, the individual must exhale completely before entering the water. However, residual volume, the volume of air that always remains in the respiratory system, must also be accounted for.By comparing an individual's in-air weight to their underwater weight, their total body volume can be determined. The density of the body D_b excluding any air in the respiratory system is calculated with the in-air mass of the individual m_air, the individual's total body volume V_total, and an estimate of residual volume V_res by:

Db=mairVtotal-VresEquation 1Body density can be used to calculate an individual's body fat composition, the percentage of total body mass that is made up of fatty tissue. Human fatty tissue has an average density of 0.9 kg/L, and the density of water is 1 kg/L. The acceleration due to gravity is 10 m/s².
Adapted from Siri, WE, Body composition from fluids spaces and density. Nutrition 1956 Springer Nature.
-A 0.3-kg object with half the density of human fatty tissue is placed in water. Ignoring the atmospheric pressure, what percentage of the mass will be submerged?

Quizplus · Accepted Answer

11ecba2d_12f5_6768_a3bf_5b4c6c51b5ef_MD0008_00 According to the Archimedes principle, an object in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. If the object's density is less than the fluid's density, the object will float at the surface because the buoyant force is in equilibrium with the weight of the object. For a floating object, the fraction submerged is equal to the ratio of the object's density to the fluid's density: 11ecba2d_12f5_6769_a3bf_7516ff235262_MD0008_00 fraction submerged=ρobjectρfluid The density of human fat is given in the passage as 0.9 kg/L, and the object's density is half this value; ρ_object is 0.45 kg/L. Because the object is less dense than water (ρ_water is 1 kg/L), the object will float at the surface and be partially submerged. Using these values, the fraction submerged is: 11ecba2d_12f5_676a_a3bf_e1bc00461140_MD0008_00 Therefore, 45% of the object will be submerged. (Choice A) The fraction submerged depends on the density of the object, not its mass. (Choice C) If the density of fat is used as the density of the object, the incorrectly calculated percent submerged would be twice as large, or 90%. (Choice D) If the density of the object is greater than or equal to the density of the fluid, the object will be fully (100%) submerged. The given object is less dense than water and therefore will be only partially submerged. Educational objective: An object floats at the surface of a fluid if its density is less than that of the fluid. The fraction submerged is equal to the ratio of the object's density to the fluid density.

Passage Hydrostatic Weighing Is a Technique Used to Determine an Individual's