Archimede’s principle states that the mass of a floatingobject equals the mass o

Question

Archimede’s principle states that the mass of a floatingobject equals the mass of the fluid displaced by the object. A 150lbm swimmer is floating in a near-by pool. 5% of her body volume isabove the surface of the water. What is the swimmer’sdensity?
water density : 0.036 lbm in^-3.

(a) Sketch the situation, clearly identifying all variables ofinterest with an appropriate symbol and associated units.
(b) Develop an equation to calculate the swimmer’s density interms of symbols only.
(c) Show the values you would use for each symbol in your equationin terms of values given and appropriate conversion factors tocalculate the density in SI units.

Explanation / Answer

Okay, so from Archimedes' Principle, you know that the swimmer has displaced water mass equal to her body mass that is below water.  Since she weighs 150 lbm and has 5% of her body above water, we know that she has displaced 150*.95 lbm of water.  Divide the density of the water by the calculated mass of water displaced, and you will have the volume of water displaced.  That will be equal to 95% of the volume of the swimmer.  So, we can find the volume of the swimmer, and take her mass again and divide it by the volume to get her density.

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