Question

In an immersion measurement of a woman’s density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L, is she able to float without treading water with her lungs filled with air?

(a) 61.915 kg
(b) 1.5 m³
(c) 41.28 kg/m³
(d) No, she cannot float with lungs filled with air.

Answer 1

A woman's density can be calculated by applying the principles of buoyancy. Her mass of water displacement is 61.915 kg, her volume is 0.0619 m³, and her density is 1000.65 kg/m³. She cannot float with her lungs filled with air.

Step-by-step explanation:

To answer these questions, we need to apply the principles of buoyancy. Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object. (a) The mass of water displaced by the woman can be calculated by subtracting her apparent mass from her mass in air: Mass of water displaced = Mass in air - Apparent mass = 62.0 kg - 0.0850 kg = 61.915 kg. (b) The volume of the woman can be calculated by dividing the mass of water displaced by the density of water: Volume = Mass of water displaced / Density of water = 61.915 kg / 1000 kg/m³ = 0.0619 m³. (c) The density of the woman can be calculated by dividing her mass in air by her volume: Density = Mass in air / Volume = 62.0 kg / 0.0619 m³ = 1000.65 kg/m³. (d) The density of air is much smaller than the density of water, so the woman would not be able to float without treading water with her lungs filled with air. Therefore, the answer is No, she cannot float with lungs filled with air.