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.

1.

If a 73.0 kg 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?

2.If, as is typical, only 22.0 % 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

1.)
Mass of Hiker , m = 73 kg
Given 1 bar = 140 Calories = 140*4186 J
1 bar = 586040 J

Now the total gravitational Potential Energy = 586040 J
m*g*h = 586040
h = 586040 / (9.8*73)
h = 819.2 m

Height of mountain hiker should climb, h = 819.2 m

2.)

If Only 22% of the Food Calories go into Mechancal Energy.
Then Total Energy released = 0.22 * 586040 J

Now the total gravitational Potential Energy = 128928.8 J
m*g*h = 128928.8
h = 128928.8 / (9.8*73)
h = 180.2 m

Height of mountain hiker nee to climb, h = 180.2 m

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