3. There are several techniques for determining bodycomposition. One method is hydrostatic weighing, or “underwaterweighingâ€. To do this measurement, the person is weighed whilestanding in air on a regular scale and weighed again whilecompletely immersed in water. By comparing these scale readings,the average density of the person can be calculated. From thatdensity, the body fat percentage of the person can be calculated.Imagine you are a physical therapist, determining the bodycomposition of a patient. The scale reading of your patientstanding in air on a regular scale is 177 pounds, and whilecompletely immersed in water is 2.5 pounds. NOTE: In this problem,a fair amount of precision is needed, so please: use g = 9.8 m/s2 ,not the estimate of 10 m/s2 for converting units of force, use 1.0pound = 4.45 Newtons
(a) Draw two free body diagrams of the patient: one when theyare weighed in air on a regular scale, and one when they areweighed while immersed in water. Label each of the forces with itsname.
(b) Determine the magnitude of each of the forces on yourdiagrams. (Recall the magnitude of a force is how big that forceis.) Include units!
(c) Determine the mass of your patient. Include units!
(d) Determine the density of your patient. Give your answer bothkilograms per cubic meter and in grams per cubic centimeter.Include units!
The body is made up of essentially two components: fat mass (thetotal fat of an individual) and fat-free mass (everything else:bone, water, lean tissue, etc.) Studies have determined that thedensities of these two components are: Density of fat mass = 0.90grams per cc Density of fat-free mass = 1.10 grams per cc (Inphysics, we write cubic centimeter as cm3 . In medicine, cubiccentimeter is written as cc.) A person with a density of 0.90 g/ccwould have 100% body fat, and a person with a density of 1.10grams/cc would have zero percent body fat. Real people fall betweenthese two extremes.
(e) Given the above information, assess your result for yourpatient’s density. Do you have confidence that your answer isreasonable? Explain why or why not.
(f) You discover that the scale reading of 2.5 pounds wasactually obtained with the patient submerged in seawater, not freshwater. Which of the following is true? Circle one answer.Explain.
A. The calculated value of density is higher than the person’sactual density.
B. The calculated value of density is lower than the person’sactual density.
C. The patient’s density would be calculated correctly
