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 bone sample (specific gravity = 3) completely immersed in isopropyl alcohol (specific gravity = 0.8) is subject to a buoyant force of 4 N. What buoyant force would the same bone sample experience when immersed in water?

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 bone sample (specific gravity = 3) completely immersed in isopropyl alcohol (specific gravity = 0.8) is subject to a buoyant force of 4 N. What buoyant force would the same bone sample experience when immersed in water?

Quizplus · Accepted Answer

11ecba2d_12f6_c704_a3bf_c3ddc5655bc7_MD0008_00 The specific gravity of a liquid or solid substance is the ratio of its density to the density of water: 11ecba2d_12f6_c705_a3bf_b9846460e278_MD0008_00 The density of isopropyl alcohol ρ_alcohol is calculated from the specific gravity of isopropyl alcohol given in the question and the value of ρ_water given in the passage: 11ecba2d_12f6_ee16_a3bf_bd30b1c463dc_MD0008_00 11ecba2d_12f6_ee17_a3bf_bfa7645e2e0a_MD0008_00 According to Archimedes principle, a submerged object experiences an upward buoyant force F_B equal to the weight of the displaced fluid, which is the product of the fluid density ρ, the displaced volume V, and the gravitational acceleration g: 11ecba2d_12f6_ee18_a3bf_d76e0c5bacf5_MD0008_00 For an object fully immersed in two different fluids (1 and 2), the volumes of fluid displaced in each are equal to the volume of the object: V₁ = V₂ = V_object. Therefore, the ratio of buoyant forces is equal to the ratio of fluid densities: 11ecba2d_12f6_ee19_a3bf_d11b3d08f3df_MD0008_00 Because the bone sample is fully immersed in isopropyl alcohol and water, the above relationship applies: 11ecba2d_12f6_ee1a_a3bf_238b8e027788_MD0008_00 The buoyant force in water F_B,water is calculated using the value of F_B,alcohol given in the question, 0.8 kg/L for ρ_alcohol, and the value of ρ_water given in the passage: 11ecba2d_12f6_ee1b_a3bf_c58c963c8b5b_MD0008_00 11ecba2d_12f7_152c_a3bf_896abb908886_MD0008_00 The buoyant force experienced by the bone in water is 5 N. (Choices A and B) Because the buoyant force is proportional to the density of the fluid, and water is denser than isopropyl alcohol, the buoyant force in water must be greater than the buoyant force in isopropyl alcohol. (Choice D) The buoyant force acting on a fully immersed object is independent of the density of the object. Educational objective: The magnitude of the buoyant force exerted on a submerged object is the product of the fluid's density ρ, the volume displaced V, and the gravitational acceleration g: F_B = ρVg. For an object fully immersed in two different fluids, the ratio of the buoyant forces is equal to the ratio of the fluid densities.

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