Q&A: Physics: Archimedes Principle?

Question by Christopher: Physics: Archimedes Principle?
The dry weight of a man is 845 N. When he is submerged underwater, the reading on the scale is only 43.2 N. (a) What is the volume of the man? (b) What is the density of the man? (c) The density of fat is 209 kg/m3, and the density of the “lean” parts of the human body (muscle, bones, and so on) is 2670 kg/m3. What percentage of the man’s body mass is “lean body mass”?
Please provide answers to A&B only, C is not needed, plus provide any equations, I need to show my work. Thanks in advance!!! Happy holidays.

Best answer:

Answer by M M
well if archimedes principle is that the upward buoyancy force is equal to the downward force of the amount of water that has been displaced (ie. its weight), then the upward force must be 845N – 43.2N

you therefore know the weight of the water that has been displaced and can find its mass from F=Mg, so if you know what the water’s density is (1000Kg per cubic metre), you know what volume of water this corresponds to (since density = mass / volume).
this volume must be equal to the man’s volume.

you know the man’s weight is 845N so from f=mg you can work out his mass. You know his volume since this is the volume of water displaced so you can use his mass and volume to find his density.

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