A 58-kg woman cheats on her diet and eats a 565-Calorie (565 kcal) jelly doughnu

Question

A 58-kg woman cheats on her diet and eats a 565-Calorie (565 kcal) jelly doughnut 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 28% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?
stairs

Explanation / Answer

(a) 4.184 J = 1 cal 540 kcal * (1000 cal/kcal) * 4.184 J/cal = 2.26 x 10^6 J (b) Gravitational Potential energy = mgh = energy burned by stairs: mgh = 2.26 x 10^6 h = (2.26 x 10^6)/((58)(9.8)) = 3796 m * (stair/0.15 m) = 26507 stairs (c) Now we have: mgh = (0.29)(2.26 x 10^6) h = ((2.26 x 10^6)(0.29))/((58)(9.8)) = 1153 m * (stair/0.15 m) = 7687 stairs

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