Question

3. There are several techniques for determining body composition. One method is hydrostatic weighing, or “underwater weighing”. To do this measurement, the person is weighed while standing in air on a regular scale and weighed again while completely immersed in water. By comparing these scale readings, the average density of the person can be calculated. From that density, the body fat percentage of the person can be calculated. Imagine you are a physical therapist, determining the body composition of a patient. The scale reading of your patient standing in air on a regular scale is 177 pounds, and while completely 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 1.0 pound = 4.45 Newtons

(a) Draw two free body diagrams of the patient: one when they are weighed in air on a regular scale, and one when they are weighed while immersed in water. Label each of the forces with its name.

(b) Determine the magnitude of each of the forces on your diagrams. (Recall the magnitude of a force is how big that force is.) Include units!

(c) Determine the mass of your patient. Include units!

(d) Determine the density of your patient. Give your answer both kilograms per cubic meter and in grams per cubic centimeter. Include units!

The body is made up of essentially two components: fat mass (the total fat of an individual) and fat-free mass (everything else: bone, water, lean tissue, etc.) Studies have determined that the densities of these two components are: Density of fat mass = 0.90 grams per cc Density of fat-free mass = 1.10 grams per cc (In physics, we write cubic centimeter as cm3 . In medicine, cubic centimeter is written as cc.) A person with a density of 0.90 g/cc would have 100% body fat, and a person with a density of 1.10 grams/cc would have zero percent body fat. Real people fall between these two extremes.

(e) Given the above information, assess your result for your patient’s density. Do you have confidence that your answer is reasonable? Explain why or why not.

(f) You discover that the scale reading of 2.5 pounds was actually obtained with the patient submerged in seawater, not fresh water. Which of the following is true? Circle one answer. Explain.

A. The calculated value of density is higher than the person’s actual density.

B. The calculated value of density is lower than the person’s actual density.

C. The patient’s density would be calculated correctly

Answer 1