49 kg woman cheats on her diet and eats a 477 Calorie (540 kcal) jelly donut for

Question

49 kg woman cheats on her diet and eats a 477 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 25% 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 = 49 kg energy equivalent of the doughnut E = 477 kcal = 477*10^3 cal .................................................................................... a) energy equivalent of one jelly doughnut in joules is E = (477*10^3 cal)(4.186 J / 1 cal) = 1996722 j = 1.996722*10^6 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 = (1.996722*10^6 J) / (47 kg)(9.8 m/s2)(0.15 m) = 28900.30 stairs = 2.89003 * 10^4 stairs c) mechnical energy E ' = 25 % of E = 0.25 E mechnical energy E ' = N'(mgh) N' = E' / mgh = (0.25 E) / (mgh) = (0.2)[E / mgh] = (0.2)N = (0.25)(28900.30) = 7225.076 stairs = 7.225076*10^3 stairs

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