Question
(a) How long will the energy in a 1470-kJ (350-kcal) cup of yogurt last in a woman doing work at the rate of 150 W with an efficiency of 20.0% (such as in leisurely climbing stairs)? (b) Does the time found in part (a) imply that it is easy to consume more food energy than you can reasonably expect to work off with exercise?
Final Answer
- Food has a lot of energy which is only slowly expended by exercise. Yes, it's easy to consume more food energy than can be expended by exercise.
Solution video
OpenStax College Physics for AP® Courses, Chapter 15, Problem 8 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A woman consumes 1470 kilojoules of energy from a cup of yogurt and expends energy or does useful work at a rate of 150 watts with an efficiency of 20.0 percent. So this power is the useful work output divided by time and we are asked in part (a) for how long can they have this power output given this much of energy consumed? So we multiply both sides by t over P and then we get that the time is the work divided by power. Now the efficiency is the work done divided by the total energy consumed and we can re-express this work as the efficiency multiplied by the energy consumed by multiplying both sides here by Q in and then replace w—which we don't know— with this energy consumed multiplied by efficiency. So then the time then is 1470 kilojoules converted into joules and then multiplied by the efficiency of 0.200 and divided by 150 watts and that's 1960 seconds which is 32.7 minutes. And part (b) asks is it easy to consume more food than can be expended by exercise more food energy that can be expended by exercise and the answer is certainly; this one cup of yogurt is a small amount of food but it takes 32.7 minutes of vigorous exercise to expend that energy.