The food calorie, equal to 4186 J, is a measure of how much energy is released w

Question

The food calorie, equal to 4186 J, is a measure of how much energy is released when food is metabolized by the body. A certain brand of fruit-and-cereal bar contains 150 food calories per bar.

a) If a 75.0kg hiker eats one of these bars, how high a mountain must he climb to "work off" the calories, assuming that all the food energy goes only into increasing gravitational potential energy?

b) If, as is typical, only 25.0% of the food calories go into mechanical 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. A person's "metabolic efficiency" is the percentage of calories eaten that are actually used; the rest are eliminated by the body. Metabolic efficiency varies considerably from person to person.)

Explanation / Answer

a) we have by energy balance,

150*4186 = 75*9.8*h (energy released by bar = gravitational potential energy = mgh)

h = 854.28 m

b) 0.25*150*4186 = 75*9.8*h

h = 213.57 m

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