A 63-kg woman eats a 566 Calorie (566 kcal) jelly doughnut for breakfast. (a) Ho
ID: 1578371 • Letter: A
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? stairsExplanation / 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.