A 64 - kg woman eats a 561 Calorie (561 kcal) jelly doughnut for breakfast. (a)

Question

A 64 - kg woman eats a 561 Calorie (561 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? 2347 Your response is off by a multiple of ten. J (b) How many steps must the woman climb on a very tall stairway to change the gravitational potential energy of the woman - Earth system by a value 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 potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast? stairs

Explanation / Answer

(a)

energy= 561 kcal= 561*10^3 cal
energy in joules is,
E = (561*10^3 cal)(4.186 J / 1 cal)
= 1933932 J
= 1.9339*10^6 J
(b)
work done is

W = N(mgh)
number of stairs is

N = work done / mgh
= (1933932) / (64)(9.8)(0.15)
= 44420 stairs
= 4.442* 10^4 stairs
(c)
mechnical energy is

E' = 22 % of E
= 0.22 E
mechnical energy

E ' = N'(mgh)

So the number of stairs is
N' = E' / mgh
= (0.22 E) / (mgh)
= (0.22)[E / mgh]
= (0.22)N
= (0.22)(44420)
= 9772.4 stairs
= 9.77*10^3 stairs

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