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 140 food calories per bar.

a) If a 66.0kg 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 20.0{ m \%} 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

considerably from person to person.)

Energy in joules = 140 x 4186 = 586040 Joules

a.
Now, we have,
E = mgh
586040 = 66 x 9.8 x h
Height = h= 906.1 meters

b
E = 0.2 x 586040 = 117208 Joules
Now, E = mgh'
117208 = 66 x 9.8 x h'
Height = 181.2 meters

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