A 66 kg woman cheats on her diet and eats a 475 Calorie (540 kcal) jelly donut f
ID: 2022595 • Letter: A
Question
A 66 kg woman cheats on her diet and eats a 475 Calorie (540 kcal) jelly donut for breakfast.(a) How many joules of energy are the equivalent of one jelly doughnut?
? J
(b) How many stairs must the woman climb to perform an amount of mechanical work equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 cm.
?stairs
(c) If the human body is only 20% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?
?stairs
Explanation / Answer
mass of the woman m = 66 kg energy equivalent of the doughnut E = 475 kcal = 475*103 cal .................................................................................... a) energy equivalent of one jelly doughnut in joules is E = (475*103 cal)(4.186 J / 1 cal) = 1988.35*103 J = 1.988*106 J b) the height of a single stair h = 15 cm = 0.15 m work done E = N(mgh) number of stairs N = work done / mgh = (1.988*106 J) / (66 kg)(9.8 m/s2)(0.15 m) = 20490.62 stairs = 2.049*104 stairs = 2.049*104 stairs c) mechnical energy E ' = 20 % of E = 0.2 E mechnical energy E ' = N'(mgh) N' = E' / mgh = (0.2 E) / (mgh) = (0.2)[E / mgh] = (0.2)N = (0.2)(20490.62) = 4098.12 stairs= 4.098*103 stairs
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