A 62.0-kg woman cheats on her diet and eats a 676-Calorie (676 kcal) jelly dough

Question

A 62.0-kg woman cheats on her diet and eats a 676-Calorie (676 kcal) jelly doughnut for breakfast.

(a) How many joules of energy are the equivalent of one jelly doughnut? (in 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 27% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?
stairs

Explanation / Answer

A.

we know that

1 cal = 4.186 J

So,

676 k-cal = 676*10^3*4.186

676 k-cal = 2.83*10^6 J

B.

Potential energy required for one step will be

E = m*g*h

Suppose she needs to climb n steps then

E = n*m*g*h = 2.83*10^6 J

n = (2.83*10^6)/(62*9.81*0.15)

n = 31020 stairs

C.

if efficieny is 27% then total energy will be

Enet = 0.27*E

0.27*E = n*m*g*h

n = 0.27*2.83*10^6/(62*9.81*0.15)

n = 8375 steps

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