A 62.0-kg woman cheats on her diet and eats a 666-Calorie (666 kcal) jelly dough

Question

A 62.0-kg woman cheats on her diet and eats a 666-Calorie (666 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 29% 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 = 62 kg
energy equivalent of the doughnut E = 666 kcal
= 666*10^3 cal
....................................................................................
a)
energy equivalent of one jelly doughnut in joules is
E = (666*10^3 cal)(4.186 J / 1 cal)
= 2787876 j
= 2.79 *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
= (2.79*10^6 J) / (62 kg)(9.8 m/s2)(0.15 m)
= 3.06 * 10^4 stairs
c)
mechnical energy E ' = 29 % of E
= 0.29 E
mechnical energy E ' = N'(mgh)
N' = E' / mgh
= (0.29 E) / (mgh)
= (0.29)[E / mgh]
= (0.29)(3.06*10^4)
= 8874 stairs

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