6.23) In a measurement of a man's density he is found to have a mass of 65.0 kg in air and an apparent mass of 1.50 kg when completely submerged in water with his lungs empty.
a. What mass of water does he displace?
b. What volume of water does he displace?
c. Calculate his density.
d. If his lungs capacity is 2.0 liters, is he able to float with his lungs filled with air without treading water?
Note: Guys help me, provide me an answer with solution/formula. Thanks!!!?
According to a now deceased physicist and mathematician in Sicily called Archimedes the force up on a body in a fluid is the volume of fluid displaced times the density of the fluid times g.
a. 65-1.5 = 63.5 kg lost = Mass of water disp.
b. M = V*D.
63.5 = V*1000,
V = 0.0635 m^3 = Vol. of water disp. = Vol. of man.
c. M = V*D.
65 = 0.0635*D,
D =
To solve these questions, we can use the principle of buoyancy and Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
a. To find the mass of water displaced, we need to calculate the difference in mass before and after submerging in water. The mass of water displaced is equal to the apparent mass in air minus the mass in water:
Mass of water displaced = Mass in air - Mass in water
Mass of water displaced = 65.0 kg - 1.50 kg
Mass of water displaced = 63.50 kg
b. The volume of water displaced can be calculated by dividing the mass of water displaced by the density of water. The density of water is approximately 1000 kg/m³:
Volume of water displaced = Mass of water displaced / Density of water
Volume of water displaced = 63.50 kg / 1000 kg/m³
Volume of water displaced = 0.0635 m³ or 63.5 liters
c. The density of the man can be calculated by dividing his mass by his volume:
Density = Mass / Volume
Density = 65.0 kg / 0.0635 m³
Density = 1023.62 kg/m³
d. To determine if the man is able to float with his lungs filled with air, we need to compare his density to the density of water. If his density is less than the density of water (1000 kg/m³), he will float without treading water. However, if his density is greater, he will sink.
The man's density is 1023.62 kg/m³, which is greater than the density of water (1000 kg/m³). Therefore, he would not be able to float with his lungs filled with air without treading water.
Remember to always double-check the values and units used in the calculations to ensure accuracy.