A 46 kg woman cheats on her diet and eats a 503 Calorie (503 kcal) jelly donut f

Question

A 46 kg woman cheats on her diet and eats a 503 Calorie (503 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 30% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast? stairs

Explanation / Answer

(a) Since 1 cal = 4.184 J

503 kcal = 503,000 cal = 2.104552 x 106 joules

(b) Height of 1 stair step is 0.15 m

E = mgh = 2.104552 x 106 joules

m = 46 kg (weight of the woman)
g = 9.82 m/s²

Now solve for h

h = 4.658 x 103 m or 3.1053 x 104 stair steps

or 31053 complete stair steps

(c) if the body is only 30% efficient, then

E(mechanical) = 0.30 *2.104552 x 106 joules = 631200 joules

h = E(mechanical)/mg = 1397 m or 9315 stair steps

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