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 Db excluding any air in the respiratory system is calculated with the in-air mass of the individual mair, the individual's total body volume Vtotal, and an estimate of residual volume Vres by:Db=mairVtotal−Vres𝐷b=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. Question 14A 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?A.2.4 NB.4.0 NC.5.0 ND.12 N
Question
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 Db excluding any air in the respiratory system is calculated with the in-air mass of the individual mair, the individual's total body volume Vtotal, and an estimate of residual volume Vres by:Db=mairVtotal−Vres𝐷b=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. Question 14A 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?A.2.4 NB.4.0 NC.5.0 ND.12 N
Solution
The buoyant force experienced by an object submerged in a fluid is given by the equation:
F = ρ * V * g
where: F is the buoyant force, ρ is the density of the fluid, V is the volume of the object, and g is the acceleration due to gravity.
In this case, the bone sample experiences a buoyant force of 4 N when submerged in isopropyl alcohol, which has a specific gravity of 0.8. Specific gravity is a ratio of the density of a substance to the density of a reference substance, in this case, water. Therefore, the density of isopropyl alcohol is 0.8 * the density of water.
We can rearrange the equation for buoyant force to solve for the volume of the bone sample:
V = F / (ρ * g)
Substituting the given values:
V = 4 N / (0.8 * density of water * 10 m/s²)
We want to find the buoyant force the bone sample would experience when submerged in water. We can use the same equation for buoyant force, but this time, the density of the fluid is the density of water:
F = ρ * V * g
Substituting the values:
F = density of water * V * 10 m/s²
Since the volume V is the same in both cases, and the density of water is 1 (by definition), the buoyant force F when the bone sample is submerged in water is the same as when it is submerged in isopropyl alcohol.
Therefore, the answer is B. 4.0 N.
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