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?
1. $9.57 \textrm{ min}$
2. $69.4 \textrm{ flights}$
Solution Video

# OpenStax College Physics Solution, Chapter 7, Problem 44 (Problems & Exercises) (2:15)

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This is College Physics Answers with Shaun Dychko. This person has a power output of 685 watts— that's the consumption that we read in table [7.5] for climbing the stairs at a rate of 116 steps per minute— and the energy they are gonna use is that of a 10-gram bit of butter which we are told has 93.0 kilocalories. This is a food calorie and example [7.1] tells us how to convert kilocalories into joules by saying there's 1 kilocalorie in every 4184 joules. So when you multiply these, the kilocalories cancel leaving us with joules and that is 3.891 times 10 to the 5 joules. So we have converted this kilocalorie unit into an <i>mks</i> unit—meters, kilograms or seconds unit— metric unit in other words. Now joules isn't written with meters, kilograms, and seconds but it can be reduced to those. It's newtons times meters because you get it by going work equals force times distance and then force is itself <i>ma</i> and so it's kilograms times meters per second squared times the meters from this distance and so yeah, joules is an <i>mks</i> unit and that's what we need in our formulas. So we have that power is the rate at which energy is used so <i>E</i> divided by <i>t</i> in other words and we can solve this for time by multiplying both sides by <i>t</i> divided by <i>P</i> and we are left with the time is the energy divided by the power. So that's 3.891 times 10 to the 5 joules divided by 685 watts which is 568 seconds which we convert into 9.57 minutes. So they can climb the stairs for 9.57 minutes after eating 10 grams of butter. And the number of flights that they will climb is 116 stairs every minute multiplied by the number of minutes giving us the total number of stairs that they will climb and then multiply by 1 flight for every 16 stairs and this will give us 69.4 flights.