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.

Part A

If a 75.0 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?

Part 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.)

Part 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

Calories per bar = 140 Bar

1 food calorie is equal to 4186 J,

Total energy released = 4186 * 140 J
Total energy released = 586040 J

(A)
m = 75.0 kg
Using Energy conservatin,
Energy available = Gravitational Potential ENERGY gained after clmbing
586040 = m*g*h
586040 = 75*9.8*h
h = 797.3 m

(B)

If only 25% of the food calories go into mechanical energy, then energy available = 0.25 * 586040 = 146510 J
Height the man can climb = (146510) / (75 * 9.8)
Height the man can climb = 199.3 m

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