A 54.0-kg woman cheats on her diet and eats a 641-Calorie (641 kcal) jelly dough

Question

A 54.0-kg woman cheats on her diet and eats a 641-Calorie (641 kcal) jelly doughnut for breakfast.

(a) How many joules of energy are the equivalent of one jelly doughnut?

(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.

(c) If the human body is only 31% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?

Explanation / Answer

(a) Since 1 cal = 4.184 J

641 kcal = 641,000 cal = 2.681 x 106 joules

(b) Height of 1 stair step is 0.15 m

E = mgh = 2.681 x 106 joules

m = 54 kg (weight of the woman)
g = 9.82 m/s²

Now solve for h

h = 5.066 x 103 m or 3.3774 x 10^4 stair steps

or 33,774 complete stair steps

(c) if the body is only 31% efficient, then

E(mechanical) = 0.31 * 2.681 x 106 joules = 831110 joules

h = E(mechanical)/mg = 1570 m or 10,470 stair steps

The rest of the energy is converted to heat of course, which the woman sweats away while climbing the steps.

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