Question

To determine an athlete's body fat, she is weighed first in air and then again while she's completely underwater. It is found that she weighs 690 N when weighed in air and 42 N when weighed underwater. What is her average density?

Answer 1

To determine the athlete's average density, calculate the mass of water displaced based on the difference in weight in air and underwater, then calculate the volume from the mass and finally divide the mass in the air by this volume.

Step-by-step explanation:

To determine an athlete's average density, the athlete is weighed in air and underwater, and the difference in weights is used to calculate the volume of water displaced. This principle is based on 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.

In this problem, the athlete's weight in air is 690 N and her weight underwater is 42 N. The weight of the water displaced is then 690 N - 42 N = 648 N. Recall that the force due to gravity is mass times the acceleration due to gravity, and since the acceleration due to gravity is approximately 9.8 m/s2, we can convert the weight of the displaced water to mass by dividing by 9.8 m/s2. The mass of the water displaced is 648 N / 9.8 m/s2 = 66.1 kg.

Since the density of water is 1000 kg/m3, the volume of water displaced, which is also the athlete's volume, is 66.1 kg / 1000 kg/m3 = 0.0661 m3. Finally, the athlete's density can be calculated using her mass in air (which corresponds to the weight of 690 N / 9.8 m/s2 = 70.4 kg) divided by her volume, yielding 70.4 kg / 0.0661 m3 = 1064 kg/m3.