The average human has a density of 950 kg/m3 after inhaling and 1018 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 lake with a water density of about 1230 kg/m3) in each of these cases?
After Inhaling (%)and After Exhaling (%)
Let V be the volume of the body.
Let v' be the volume of the body displaced.
densitywater*v'=densitybody*V
solve for v'/v
To calculate the percentage of the human body that would be above the surface in the Dead Sea, we need to compare the density of the human body with the density of the water.
Let's start with the case after inhaling:
1. Calculate the average density of the human body after inhaling:
- The average density of the human body after inhaling is given as 950 kg/m³.
2. Calculate the percentage of the human body that would be above the surface:
- Divide the density of the human body after inhaling by the density of the water in the Dead Sea:
Percentage after inhaling = (Density of human body after inhaling / Density of water in Dead Sea) * 100
Next, let's calculate the case after exhaling:
1. Calculate the average density of the human body after exhaling:
- The average density of the human body after exhaling is given as 1018 kg/m³.
2. Calculate the percentage of the human body that would be above the surface:
- Divide the density of the human body after exhaling by the density of the water in the Dead Sea:
Percentage after exhaling = (Density of human body after exhaling / Density of water in Dead Sea) * 100
Plug in the given values and calculate the percentages for each case.