Respuesta :
Answer:
a) [tex]E=2.616\times 10^6 \textup{ J}[/tex]
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
[tex]E = 459\times 10^3 \ cal[/tex]
[tex]E = (625\times 10^3 \textup{ cal})(\frac{ 4.186 \textup{ J}}{1\textup{ cal}}) = 2616250\textup{ J}[/tex]
or
[tex]E=2.616\times 10^6 \textup{ J}[/tex]
(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,
[tex]n = \frac{W}{mgh}[/tex]
or
[tex]n = \frac{2616250 \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}[/tex]
or
n = 26966.08 ≅ 26966 stairs
(c) The number of steps climbs by woman when the body is 26% efficient:
[tex]n = \frac{(0.26)W}{mgh}[/tex]
Therefore, number of steps:
[tex]n = \frac{(0.26)(2616250) \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}[/tex]
or
n = 7011.18 ≅ 7012 stairs
