Question
(a) How long can you rapidly climb stairs (116/min) on the 93.0 kcal of energy in a 10.0-g pat of butter? (b) How many flights is this if each flight has 16 stairs?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 7, Problem 44 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. In this question, we are going to figure out for how long someone could climb stairs at a rate of 116 steps per minute using the energy in 10 grams of butter? So this butter has 93.0 kilocalories of energy and we need to convert that into joules by multiplying by 4184 joules per kcal— that's a conversion factor that we saw used in example [7.1]— and we need m.k.s units for our formulas— that is meters, kilograms and seconds— and so joules is an m.k.s unit because it works out to kilograms meters per second squared times meters... this part here is Newtons, which is mass times acceleration and then multiplying that by distances... how you calculate energy or work done: force times distance. Okay! So joules is kilograms meters squared per second squared, in other words, which is to say it is an m.k.s unit— it's a metric unit— and that's what we need for our formulas. Okay so that's 3.891 times 10 to the 5 joules of energy in 10 gram pat of butter. The power output is 685 watts, which we look up in this table [7.5] where we have 685 watts is the power for climbing stairs at 116 steps per minute. And then we can say power is the rate of energy use or energy divided by time in other words and we can solve this for t to answer this question. So we multiply both sides by t divided by P and then the power cancels on the left, time cancels on the right and we are left with time equals energy divided by power. So that's 3.891 times 10 to the 5 joules divided by the 685 watts which is 568 seconds, which is easier to understand if we convert it into minutes so multiply by 1 minute for every 60 seconds and we are left with 9.47 minutes. And part (b) asks how many flights can you climb during this 9.47 minutes? So if we are climbing 116 steps per minute that gives us the total number of steps up to this point, minutes cancel because they are on opposite sides of this fraction and then we have 1 flight for every 16 steps or stairs, whichever word you prefer, and this works out to 68.6 flights.