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Question
Body fat is metabolized, supplying 9.30 kcal/g, when dietary intake is less than needed to fuel metabolism. The manufacturers of an exercise bicycle claim that you can lose 0.500 kg of fat per day by vigorously exercising for 2.00 h per day on their machine. (a) How many kcal are supplied by the metabolization of 0.500 kg of fat? (b) Calculate the kcal/min that you would have to utilize to metabolize fat at the rate of 0.500 kg in 2.00 h. (c) What is unreasonable about the results? (d) Which premise is unreasonable, or which premises are inconsistent?
Question Image
<b>Table 7.5</b> Energy and oxygen consumption rates of typical human activities.
Table 7.5 Energy and oxygen consumption rates of typical human activities.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
  1. $4650 \textrm{ kcal}$
  2. $38.8 \textrm{ kcal/min}$
  3. The power consumption in units of watts is $2700 \textrm{ W}$. This is 46% greater than that of a professional cyclist. This is unreasonable.
  4. Presuming that such a high power consumption can be sustained for 2 hours is unreasonable.
Solution Video

OpenStax College Physics Solution, Chapter 7, Problem 66 (Problems & Exercises) (2:39)

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Video Transcript

This is College Physics Answers with Shaun Dychko. In this question we are going to examine the claim by this bicycle manufacturer that you can burn 0.500 kilograms of fat per day by exercising vigorously for 2 hours. So let's first find out how many kilocalories are in half a kilogram of fat. So we multiply by 9.3 kilocalories per gram and then convert these grams into kilograms by multiplying by 1000 grams per kilogram and all these units cancel leaving us with kilocalories so that is 4650 kilocalories in half a kilogram of fat. Now in part (b), we are going to calculate the number of kilocalories burned per minute in order to metabolize fat at a rate of 0.500 kilograms for every 2 hours because that's the claim; the claim is if you exercise vigorously, you can burn this much fat in 2 hours. So we have calculated that this much fat— half a kilogram—is the same as 4650 kilocalories so we divide that by 2 hours and then multiply by 1 hour for every 60 minutes and we end up with 38.8 kilocalories per minute. This is a power although the units are strange power is normally in joules per second or also known as watts and so we can make a conversion into watts in order to compare with numbers in this table [7.5] because we want to know is this number realistic—it's hard to tell— we don't have experience with kilocalories per minute so there's no way to really know offhand whether this is a realistic number or not. So we convert 38.8 kilocalories per minute into watts by multiplying by 4184 joules for every kilocalorie and then multiply by 1 minute for every 60 seconds and now we have converted the units into joules per second which is watts and that is 2700 watts. So now we can compare to this table because these numbers are in watts as well. And here's the energy consumption of a professional racer so we can expect this to be the upper limit that a human can possibly do and you know maybe there's exceptional humans of course, you know, that might go a bit higher but this number that we have here—2700—is 46% higher than that of a professional cyclist and it's unrealistic for a person to do that and especially that cannot be maintained for 2 hours as claimed by the exercise bike manufacturer.