Question

A 63-kg woman eats a 438 Calorie (438 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 26% efficient in converting chemical potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast?

Answer 1

(a) Look-into the text-book, you will find that -

1 calorie = 4.184 J

Therefore, 438 kcal = 438000 cal = 438000 x 4.184 = 1.832 x 10^6 J

(b) Now, given that height of a single stair = 15 cm = 0.15 m

E = mgh = 1.832 x 10^6 joules

m = 63 kg (weight of the woman)
g = 9.82 m/s²

Now solve for h

h = (1.832 x 10^6) / (63 x 9.82) = 2962.2 m

So, the number of steps, the woman can climb = 2962.2 / 0.15 =  19748 (Answer)

(c) Now, if the body is only 26% efficient, then

E(mechanical) = 0.26 * 1.832 x 10^6 joules = 476320 J

In this case, h = 476320 / (63 x 9.8) = 771.5 m

Hence, the no. of steps the woman can climb = 771.5 / 0.15 = 5143

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

Hope, you understand the solution!