b) How many days of a diet of 2200 large calories are equivalent to the gravitational energy change from sea level to the top of Mount Everest, 8848 m above sea level? Assume your mass is 72 kg. (The body is not anywhere near 100% efficient in converting chemical energy into change in altitude. Also note that this is in addition to your basal metabolism.)

Respuesta :

Answer:

No. of days, n = 0.68 days

Solution:

As per the question:

Energy of one day diet, [tex]E_{d} = 2200\ large\ calories[/tex]

Height above sea level, H = 8848 m

Mass, M = 72 kg

Now,

1 large calorie = [tex]4.2\times 10^{3} J[/tex]

Therefore,

[tex]E_{d} = 2200\times 4.2\times 10^{3} = 9.24\times 10^{6}J[/tex]

Now,

The potential energy required for jumping of the Mt. Everest at a height of 8848 m:

[tex]PE_{g} = MgH = 72\times 9.8\times 8848 = 6.24\times 10^{6} J[/tex]

No. of days can be given as:

[tex]n = \frac{PE_{g}}{E_{d}}[/tex]

[tex]n = \frac{6.24\times 10^{6}}{9.24\times 10^{6}} = 0.68\ days[/tex]