A 63-kg woman eats a 566 Calorie (566 kcal) jelly doughnut for breakfast. (a) Ho

Question

A 63-kg woman eats a 566 Calorie (566 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? (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 24% 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) Since 1 cal = 4.184 J

566 kcal = 566,000 cal = 2.368 x 10^6 joules

(b) Height of 1 stair step is 0.15 m

E = mgh = 2.368 x 10^6 joules

m = 63 kg (weight of the woman)

g = 9.81 m/s²

Now solve for h

h = 3.83 x 10^3 m

Thus,

No. of steps = (3.83 x 10^3)/0.15

= 25,545

(c) if the body is only 24% efficient, then

E(mechanical) = 0.24 * 2.368 x 10^6 joules = 568,320 joules

h = E(mechanical)/mg = 919.57 m

Thus,

No. of steps = 919.57/0.15

= 6130

The rest of the energy is converted to heat of course, which the woman sweats away while climbing the steps.

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