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The food calorie, equal to 4186 J, is a measure of how much energy is released when the body metabolizes food. A certain fruit­and­cereal bar contains 140 food calories. (a) If a 65­kg hiker eats one bar, how high a mountain must he climb to "work off" the calories, assuming that all the food energy goes into increasing gravitational potential energy? (b) If, as is typical, only 20% of the food calories go into mechani- cal energy, what would be the answer to part (a)? (Note: In this and all other problems, we are assuming that 100% of the food calories that are eaten are absorbed and used by the body. This is actually not true. Aperson's "metabolic efficiency" is the percentage of calories eatenthat are actually used; the rest are eliminated by the body.Metabolic efficiency varies considerably from person toperson.)

Respuesta :

cjmejiab

Our variables

[tex]E_c = 4186J[/tex]

A bar contains 140 calories.

A) When you eat a bar you gain

[tex]E= 140*4186J = 0.586*10^6[/tex] calories.

To climbing we use the equation of Potential Energy, that is,

[tex]U= mgh[/tex]

That should be the equal energy gain when you eat a fruit&cereal bar

Therefore from, [tex]U = E[/tex]

We use the equation of Potential Energy to find the high.

[tex]h= \frac{E}{mg} =\frac{140x4186}{(65x9.8)} = 920m[/tex]

B. Only 20% of food energy is available.

Then, [tex]E x 0.20 = mgh'[/tex]

Then, Height, [tex]h' = h*20\%[/tex]

[tex]h'=184m[/tex]

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