How Does Lung Capacity Affect Body Density?

[Kcoats]

In a measurement of a man's density he is found to have a mass of 58.9 kg in air and an apparent mass of 1.0 kg when completely submereged in water with his lungs empty. If his lung capacity is 1.9 liters, what is his density when his lungs are full?

Correct answer: 985 kg/m^3


Okay, here is how I have been working it. Where am I going wrong?
1.9L(1000cm^3/1L)(1m^3/100cm^3)=1.9E1

58.9 kg-1.0 kg=57.9 kg/10^3 kg/m^3=5.79E-2 kg/m^3 +1.9E1 m^3=1.90E1 m^3

58.9 kg/1.90E1 m^3=3.105E-1 kg/m^3

 

[Andrew Mason]

In a measurement of a man's density he is found to have a mass of 58.9 kg in air and an apparent mass of 1.0 kg when completely submereged in water with his lungs empty. If his lung capacity is 1.9 liters, what is his density when his lungs are full?

Correct answer: 985 kg/m^3


Okay, here is how I have been working it. Where am I going wrong?
1.9L(1000cm^3/1L)(1m^3/100cm^3)=1.9E1

58.9 kg-1.0 kg=57.9 kg/10^3 kg/m^3=5.79E-2 kg/m^3 +1.9E1 m^3=1.90E1 m^3

58.9 kg/1.90E1 m^3=3.105E-1 kg/m^3

You have to work out the volume of the man. Since his volume displaces 57.9 kg of water, his volume is 57.9 litres. If he increases that volume by 1.9 litres (to 59.8 L) but does not add weight, his density is:

58.9kg/59.8 L = .985 kg/L or 985 kg/m^3

AM

 

[thepatientmental]

Based on the given information, it seems like your calculations are correct. However, the final answer should be in kg/m^3 and not just kg/m^3. When converted, your answer of 3.105E-1 kg/m^3 is equivalent to 310.5 kg/m^3 which is not the correct answer. To get the correct answer, you need to divide the mass of 58.9 kg by the volume of 1.9 liters (or 0.0019 m^3) to get a density of 31000 kg/m^3. This is the density when his lungs are completely full. However, since we are looking for the density when his lungs are full, we need to subtract the density of air (1.2 kg/m^3) from the density of the man when his lungs are full to get the final answer of 31000 kg/m^3 - 1.2 kg/m^3 = 985 kg/m^3. This is the density of the man when his lungs are full. I hope this helps!