A useful measure of an individual's physical condition is the fraction of his or ner body that consist of fat. This problem describes a simple technique for estimating this fraction by weighing the individual twice, once in air and once submerged in water. a. A man has body mass mb = 122.5 kg. If he stands on a scale calibrated to read in newtons, what would the reading be? If he then stands on a scale while he is totally submerged in water at 30 °C (specific gravity = 0.996) and the scale reads 44.0 N, what is the volume of his body (liters)? What is his body density, po (kg/L)? b. Suppose the body is divided into fat and nonfat components, and that xf (kilograms of fat/kilogram of total body mass) is the fraction of the total body mass that is fat: Xf = Mp Prove that 1 1 Pb Xf Pnf 1 1 Ps Pnf Where Pp, Pr, and pns are the average densities of the whole body, the fat component, and the nonfat component, respectively.
A useful measure of an individual's physical condition is the fraction of his or ner body that consist of fat. This problem describes a simple technique for estimating this fraction by weighing the individual twice, once in air and once submerged in water. a. A man has body mass mb = 122.5 kg. If he stands on a scale calibrated to read in newtons, what would the reading be? If he then stands on a scale while he is totally submerged in water at 30 °C (specific gravity = 0.996) and the scale reads 44.0 N, what is the volume of his body (liters)? What is his body density, po (kg/L)? b. Suppose the body is divided into fat and nonfat components, and that xf (kilograms of fat/kilogram of total body mass) is the fraction of the total body mass that is fat: Xf = Mp Prove that 1 1 Pb Xf Pnf 1 1 Ps Pnf Where Pp, Pr, and pns are the average densities of the whole body, the fat component, and the nonfat component, respectively.
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please only a and b
Transcribed Image Text:A useful measure of an individual's physical condition is the fraction of his or
her body that consist of fat. This problem describes a simple technique for estimating
this fraction by weighing the individual twice, once in air and once submerged in water.
a. A man has body mass mb = 122.5 kg. If he stands on a scale calibrated to read in
newtons, what would the reading be? If he then stands on a scale while he is
totally submerged in water at 30 °C (specific gravity = 0.996) and the scale reads
44.0 N, what is the volume of his body (liters)? What is his body density, pb
(kg/L)?
b. Suppose the body is divided into fat and nonfat components, and that xf
(kilograms of fat/kilogram of total body mass) is the fraction of the total body
mass that is fat:
mf
Xf
Mp
Prove that
1
1
Pb
Pnf
1
1
Ps Pnf
Where Pp, Ps, and pnf are the average densities of the whole body, the fat
component, and the nonfat component, respectively.
c. If the average specific gravity of body fat is 0.9 and that of nonfat tissue is 1.1,
what fraction of the man's body in Part (a) consists of fat?
d. The body volume calculated in Part (a) includes volumes occupied by gas in the
digestive tract, sinuses, and lungs. The sum of the first two volumes is roughly
100 ml and the volume of the lungs is roughly 1.2 liters. The mass of the gas is
negligible. Use this information to improve your estimate of xf.
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