   Chapter 9, Problem 24P

Chapter
Section
Textbook Problem

The average human has a density of 945 kg/m3 after in haling and 1 020 kg/m3 after exhaling. (a) Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea (a body of water with a density of about 1 230 kg/m3) in each of these cases? (b) Given that bone and muscle are denser than fat, what physical characteristics differentiate “sinkers” (those who tend to sink in water) from “floaters” (those who readily float)?

(a)

To determine
The percentage of the human body be above the surface in Dead Sea without making any swimming movement after inhaling and after exhaling.

Explanation

Section1:

To determine: The percentage of the human body after inhaling be above the surface in Dead Sea without making any swimming movement.

Answer: The percentage of the human body after inhaling be above the surface in Dead Sea without making any swimming movement is 23.2%abovethesurface .

Explanation: For a person to be float, the buoyant force acting on him must be equal to weight of the person, or the weight of the water displaced by the person must equals his own weight that is the B=mg(ρseaVsubmerged)g=(ρbodyVtotal) and rearranging this, Vsubmerged/Vtotal is calculated.

Given info: The average human density after inhaling is 945kg/m3 and density of dead sea water is 1230kg/m3 .

The formula for the percentage of body submerged in the water is,

VsubmergedVtotal=ρbodyρsea

• ρbody is average density of human body after inhaling.
• ρsea is density of dead sea water.

Substitute 945kg/m3 for ρbody and 1230kg/m3 for ρsea to find Vsubmerged/Vtotal .

VsubmergedVtotal=945kg/m31230kg/m3=0.768=76.8%

Thus, the 76.8% of human body is submerged in the water and the remaining 23

(b)

To determine
The physical characteristics differentiate “sinkers” from “floaters”.

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