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We are going to use Eq (4-2) to solve the problem To begin with, however, we need to know that food calories are actually kilocalories So when the problem says a glass of orange juice has 120 calories, then in terms of the scientific unit of energy called calorie, this is 120,000 calories (cal), or 120 kilocalories (kcal) The amount of heat entering our athlete is 120 kcal, or 502 kJ (120 kcal 4184 kJ/kcal) Work is force times distance Therefore the amount of work done is the weight of the athlete (the force) times the distance he is lifted Converting to SI units, 225 lb is about 1000 N of force So the amount of work to lift the athlete to the 102nd floor is 1000 N (102 floors 3 m/floor) 5 306,000 Nm 5 306 kJ of work The change in the athlete s internal energy is DU 5 q 2 w 5 502 kJ 2 306 kJ 5 196 kJ The athlete s internal energy has increased (by 196 kJ) because the glass of orange juice contained more energy than is necessary to lift 225 lb to the
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chapter 4 E n E r g y a n d L i f E
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top of the Empire State Building Our athlete used up less than 2/3 the calories in the glass of orange juice If you have some concept as to what it feels like to walk up almost 2000 steps, and how you might feel after such a workout, then it may seem odd that walking up 102 flights of stairs burns off fewer calories than are in 2/3 of a glass of orange juice The apparent discrepancy (from our everyday experience) here is that we have made some simplifying assumptions that perhaps include a little too much simplification
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Simplifying Assumptions
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In science, we often make simplifying assumptions We purposely assume something to be the case, even though we know it s not true, in order to keep things simple Keeping things simple can allow us to make a calculation or discover something that we would otherwise not be able to do or discover Then, after we understand our system better, after we have calculated what we need to calculate, we can (if we choose) refine our calculations and refine our understanding by gradually removing or changing our simplifying assumptions Of course, the most important aspect of this is to know what our assumptions are and to make a judgment as to whether the assumptions are reasonable or at least practically workable By practically workable we mean that (1) even if our assumptions are wrong, we understand that they are wrong and we have some idea where they are off (or where they differ from the more correct solution) and (2) most importantly the simplifying assumptions allow us to accomplish something that we would otherwise not be able to accomplish without their help As an example of accomplishing something practical even with assumptions that are incorrect, imagine if we were to measure the energy content in food by drinking a glass of orange juice, doing some work, and seeing how much work we can get done before we get hungry again If the athlete in Prob 4-1 got hungry when he reached the top of the Empire State Building, we would say that the orange juice had 306 kJ of energy To say such a thing, we have to make some simplifying assumptions, not the least of which is the idea that the athlete could tell by his hunger when he has burned off the glass of orange juice Even so, this method still gives us some clue as to how much energy is in the orange juice Assuming the athlete can achieve some accuracy in reporting his hunger, even if the resulting energy content is way off, we can still compare various
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