Answer to Question #181524 in Physics for Kise

Question #181524

(a) What is the density (in 0 decimal place) of a woman who floats in freshwater with 4.00% of her volume above the surface?

(b) What percent (in 2 decimal places) of her volume is above the surface when she floats in seawater?


1
Expert's answer
2021-04-19T17:07:48-0400

(a) From the equilibrium of the force of gravity and the buoyancy force:


ρliquidgV(1κ)=ρbodygV,ρbody=ρliquid(1κ)=690 kg/m3.\rho_\text{liquid} gV(1-\kappa)=\rho_\text{body}gV,\\ \rho_\text{body}=\rho_\text{liquid} (1-\kappa)=690\text{ kg/m}^3.

(b) Reasoning the same way:


ρseawater(1κ)=ρbody,κ=1ρbodyρseawater=0.0625,\rho_\text{seawater} (1-\kappa)=\rho_\text{body},\\ \kappa=1-\frac{\rho_\text{body}}{\rho_\text{seawater}}=0.0625,

or 6.25%.


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