Basal metabolic rate and energy expenditure
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Basal metabolic rate and energy expenditure
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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.
A person’s Basal Metabolic Rate (BMR) is the daily amount of energy their body requires if at rest in a temperate environment. This energy is used to support the functioning of the human body, and in particular is responsible for maintaining homeostasis. Some processes that factor into the BMR of a person are things like breathing, blood circulation, nerve function, brain activity, and support of vital organs. The energy used or “burned” in these processes generally ends up in the form of heat expended by the body.
An average person’s BMR accounts for around 70% of their total daily energy expenditure, while physical activity accounts for 20% and digestion accounts for the remaining 10%. The average BMR in the United States is 6250 Joules/day for women and 6950 Joules/day for men. This information is tabulated in Table 1.
Table 1. The BMR and daily energy expenditures of American adult males and females.
A nutritionist is interested in seeing the effects of increasing physical activity on the BMR. She has one of her patients undergo an exercise involving throwing a baseball of mass .14kg into the air and catching it. After twenty minutes of this activity daily for a week, the nutritionist discovered that the patient’s BMR rose and they were beginning to lose weight. She concluded that more physical activity causes an increase the BMR, resulting in further energy expenditure during the day.
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[question] => What minimum amount of total daily energy does the average US female require to support her BMR?
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[answer] => 4
[description] => Reason for the Correct Answer:
An average person’s BMR is 70% of their total energy requirement
BMR = 0.7 x total energy expenditure
Total energy expenditure = BMR/0.7 = 6250J/0.7
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[answers] => Array
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[0] => Array
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[each_answer] => A. 6250 J/1.7
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[each_answer] => B. 6250 J x 1.7
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[2] => Array
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[each_answer] => C. 6250 J x 0.7
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[each_answer] => D. 6250 J/0.7
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => How fast would the baseball have to be going in order for its kinetic energy to equal the amount of BMR energy expended by a US male per day?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Kinetic energy = ½ mv2
The average BMR for a US male is 6950 Joules
6950 Joules = ½ mv² = ½ (0.14kg)v², so v = [2 x 6950J/0.14kg]¹/²
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[each_answer] => A. 2 x 6950J/0.14kg
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[1] => Array
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[each_answer] => B. [4 x 6250J/0.14kg]²
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[each_answer] => C. [2 x 6950J/0.14kg]¹/²
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[each_answer] => D. [2 x 6250J/0.14kg]²
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => How high would the baseball have to be tossed in the air in order for its increase in gravitational potential energy to equal the amount of BMR energy expended by a US female per day?
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[answer] => 1
[description] => Reason for the Correct Answer:
Gravitational potential energy is given by PE = mgh
The average US females BMR is 6250 Joules/day
6250 Joules = mgh = (0.14kg)(9.8 m/s²)h, so h=6250 J/(0.14kg x 9.8m/s²)
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[answers] => Array
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[each_answer] => A. 6250 J/(0.14kg x 9.8m/s²)
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[each_answer] => B. (0.14kg x 9.8m/s²)/6250 J
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[each_answer] => C. 6250 J x 0.14kg x 9.8m/s²
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[each_answer] => D. (0.14kg x 9.8m/s²)/6950 J
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[quiz_unique_key] => 2261298308
[question] => How far would a spring with spring constant k = 150 N/m have to be stretched in order for the spring to store the same amount of energy as the daily energy required to support digestion for the average US male?
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[answer] => 3
[description] => Reason for the Correct Answer:
Find the total daily energy expenditure of an average US male.
Digestion accounts for 10% of total daily energy expenditure.
The formula for spring potential energy is ½kx²
BMR accounts for 70% of total daily energy expenditure. For the average male, total daily energy expenditure would then be (6950J/0.7). Digestion accounts for 10% of total daily energy expenditure, so energy required for digestion would be (6950J/0.7) x 0.1.
The total daily energy expenditure of an average US male is 6950J/0.7, so digestion accounts for 6950J/0.7 x 0.1. This means 6950J x (0.1/0.7)= ½ (150N/m)x², so x=[2 x 6950 J x (0.1/0.7)/(150N/m)]¹/²
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[each_answer] => A. 2 x 6950 J x 0.1/(150N/m)]¹/²
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[each_answer] => B. [2 x 6950 J x 0.7/(150N/m)]¹/²
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[each_answer] => C. [2 x 6950 J x (0.1/0.7)/(150N/m)]¹/²
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[each_answer] => D. [2 x 6950 J x (0.7/0.1)/(150N/m)]¹/²
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[question] => In an effort to lose weight and burn more calories a 100kg woman is deciding which activity to perform. Which of the following processes would most likely require the most energy for the woman to perform?
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[answer] => 2
[description] => Reason for the Correct Answer:
PE(gravity) = mgh, PE(spring) = ½ kx²
Find the amount of potential energy the woman gives to the objects for each case.
Since climbing the stairs increases the gravitational potential energy by 100kg x 10m/s² x 20m=20,000J, it is by far the largest change in energy of the selections
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[answers] => Array
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[0] => Array
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[each_answer] => A. Compressing a spring (k=1,000N/m) 20 times by an amount of 0.1m
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[each_answer] => B. Walking up a 20 meter tall flight of stairs
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[2] => Array
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[each_answer] => C. Lifting a 15kg barbell 10 times by an amount of 1m into the air
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[each_answer] => D. Riding in a 350kg elevator 95 meters to the top of the building
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[556604|1] => D
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