Question

A 66-kg woman cheats on her diet and eats a 625-Calorie (625 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? 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 26% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast? stairs

Answer 1

Answer:

a) $E=2.616\times 10^6 \textup{ J}$

b) 26966 stairs

c) 7012 stairs

Explanation:

Given:

Mass of the woman =  64 kg

Energy intake =  459 kcal.

(a)Noe, the energy equivalent of one jelly doughnut can be calculated as

$E = 459\times 10^3 \ cal$

$E = (625\times 10^3 \textup{ cal})(\frac{ 4.186 \textup{ J}}{1\textup{ cal}}) = 2616250\textup{ J}$

or

$E=2.616\times 10^6 \textup{ J}$

(b) The number of steps climbed by the woman to consume one jelly doughnut of energy can be calculated as:

The gravitational potential energy to climb each step of stair case is given as:

W = mgh

where,

m = mass

g = acceleration due to gravity

h = height up to which mass is moved  

Now, Total work done to climb the n number of steps is,

            W =n(mgh)

where, n is the number of steps on stairs

on rearrange, we get,

$n = \frac{W}{mgh}$

or

$n = \frac{2616250 \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}$

or

n = 26966.08 ≅ 26966 stairs

(c) The number of steps climbs by woman when the body is 26% efficient:

$n = \frac{(0.26)W}{mgh}$

Therefore, number of steps:

$n = \frac{(0.26)(2616250) \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}$

or

n = 7011.18 ≅ 7012 stairs