A scale under water
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A scale under water
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Normal bathroom scales only give the weight of a person. This does not give one enough information to determine the body fat percentage of a person. A technique called “hydrostatic weighing” or “underwater weighing” can determine a person’s density, and therefore give information about the percent of body fat in a person’s body.
To perform hydrostatic weighing, a person is first weighed in the air while standing on a regular scale. Then the person is weighed while underwater with the air expelled from their lungs. The measured weight of a person underwater will be less than the measured weight of the person in the air because of the buoyant force acting on the person.
Figure 1. The apparatus involved in hydrostatic weighing is depicted.
Once the weights in air and water are determined, one can calculate the average density of a person. Knowing the average density of the person will allow an estimate of the body fat percentage since fat is less dense than muscle and bone. People with a high average body density have more muscle per weight and so have a smaller body fat percentage.
Consider the data below that was taken for someone using the technique of underwater weighing. (The density of the water used was 1000 kg/m³) Assume the acceleration due to gravity is 10m/s². All measurements were taken at a depth of 5m.
[post_title] => A scale under water
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[question] => What is the volume of person C?
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[answer] => 4
[description] => Reason for the Correct Answer:
F(buoyant) = ρVg
The buoyant force on person C is 684N – 54.0N = 630N
F(buoyant) = ρVg, so 630N = (1000kg/m³)(V)(9.8m/s²) which means that V = 0.0643m³
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[answers] => Array
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[each_answer] => A. 6.3 m³
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[each_answer] => B. 0.00630 m³
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[each_answer] => C. 0.630 m³
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[each_answer] => D. 0.0630 m³
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => Which person experiences the largest buoyant force while submerged in water?
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[answer] => 3
[description] => Reason for the Correct Answer:
The only forces on the person are the buoyant force, gravity, and the force exerted upward from the scale.
The buoyant force is equal to the difference between the weight in water and the weight in air.
For person C, 684N – 54.0N = 630N which is the largest buoyant force for all four people.
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[answers] => Array
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[0] => Array
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[each_answer] => A. Person A
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[1] => Array
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[each_answer] => B. Person B
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[each_answer] => C. Person C
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[each_answer] => D. Person D
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => What is the mass of person A?
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[answer] => 4
[description] => Reason for the Correct Answer:
Weight is equal to mg.
The accurate weight of a person is the weight measured in air.
Weight = mg, so 652 N = m(10m/s²), or m = 65.2kg
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[answers] => Array
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[each_answer] => A. 652.0 kg
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[each_answer] => B. 6.52 kg
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[each_answer] => C. 6520 kg
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[each_answer] => D. 65.2 kg
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[quiz_unique_key] => 2261298308
[question] => If salt water (density =1025 kg/m3) were mistakenly and unknowingly used instead of fresh water (density =1000 kg/m3) what would most likely happen to the results?
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[answer] => 3
[description] => Reason for the Correct Answer:
Muscle is more dense than fat so body fat percentage will be small for someone with a large average body density, and body fat percentage would be large for someone with a small average body fat density.
Average body density=mass/volume, and mass can be found from knowing the Weight in air=mg, which means the actual mass of the person will still be found correctly.
Using a higher density fluid will increase the buoyant force on the person.
Since the buoyant force will be larger, the volume of the person will be inferred to be larger, which means the density will seem smaller. Smaller density means larger body fat percentage.
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[answers] => Array
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[0] => Array
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[each_answer] => A. People would be measured to have a smaller body fat percentage than they actually have
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[1] => Array
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[each_answer] => B. People would be measured to have zero body fat percentage
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[2] => Array
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[each_answer] => C. People would be measured to have a higher body fat percentage than they actually have
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[each_answer] => D. People would still be measured to have the correct body fat percentage that they actually have
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[quiz_unique_key] => 574431310
[question] => In a follow-up measurement, person B was weighed at a depth of 10m, as opposed to the initial 5m. What will the new scale reading be?
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[answer] => 4
[description] => Reason for the Correct Answer:
Person B was completely submerged for both measurements
The buoyant force is equal to the weight of the fluid displaced
Person B displaced the same amount of fluid for each measurement
Since the displaced fluid will be the same for both measurements, the buoyant force and scale readings will be the same for both measurements (98.0 N). As long as the object is completely submerged, the buoyant force does not depend on the depth underwater.
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[each_answer] => A. 49.0 Newtons
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[each_answer] => B. 196.0 Newtons
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[2] => Array
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[each_answer] => C. 36.0 Newtons
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[each_answer] => D. 98.0 Newtons
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