Answer:
a) ![E=2.616\times 10^6 \textup{ J}](https://tex.z-dn.net/?f=E%3D2.616%5Ctimes%2010%5E6%20%5Ctextup%7B%20J%7D)
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 = (625\times 10^3 \textup{ cal})(\frac{ 4.186 \textup{ J}}{1\textup{ cal}}) = 2616250\textup{ J}](https://tex.z-dn.net/?f=E%20%3D%20%28625%5Ctimes%2010%5E3%20%5Ctextup%7B%20cal%7D%29%28%5Cfrac%7B%204.186%20%5Ctextup%7B%20J%7D%7D%7B1%5Ctextup%7B%20cal%7D%7D%29%20%3D%202616250%5Ctextup%7B%20J%7D)
or
![E=2.616\times 10^6 \textup{ J}](https://tex.z-dn.net/?f=E%3D2.616%5Ctimes%2010%5E6%20%5Ctextup%7B%20J%7D)
(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,
or
![n = \frac{2616250 \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B2616250%20%5Ctextup%7B%20J%7D%7D%7B%2866%5Ctextup%7B%20kg%7D%29%289.8%20%5Ctextup%7B%20m%2Fs%7D%5E2%29%280.15%5Ctextup%7B%20m%7D%29%7D)
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}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B%280.26%29W%7D%7Bmgh%7D)
Therefore, number of steps:
![n = \frac{(0.26)(2616250) \textup{ J}}{(66\textup{ kg})(9.8 \textup{ m/s}^2)(0.15\textup{ m})}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B%280.26%29%282616250%29%20%5Ctextup%7B%20J%7D%7D%7B%2866%5Ctextup%7B%20kg%7D%29%289.8%20%5Ctextup%7B%20m%2Fs%7D%5E2%29%280.15%5Ctextup%7B%20m%7D%29%7D)
or
n = 7011.18 ≅ 7012 stairs