A 48 kg woman cheats on her diet and eats a 507 Calorie (507 kcal) jelly donut f

Question

A 48 kg woman cheats on her diet and eats a 507 Calorie (507 kcal) jelly donut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? I already solved it and I got 2121288 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 21% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast? = ??? Stairs ?

Explanation / Answer

A 59 kg woman cheats on her diet and eats a 547 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 22% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?

(a) Since 1 cal = 4.184 J

547 kcal = 547,000 cal = 2.289 x 10^6 joules

(b) Height of 1 stair step is 0.15 m

E = mgh = 2.289 x 10^6 joules

m = 59 kg (weight of the woman)
g = 9.82 m/s²

Now solve for h

h = 3.95 x 10^3 m or 2.633 x 10^4 stair steps

or 26,335 complete stair steps

(c) if the body is only 22% efficient, then

E(mechanical) = 0.22 * 2.289 x 10^6 joules = 503,502.36 joules

h = E(mechanical)/mg = 869 m or 5,794 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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