# Density when lungs are full?

#### 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

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#### Andrew Mason

Science Advisor
Homework Helper
Kcoats said:
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

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