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

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 145 food calories per bar
PART A
If a 74.0 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 24.0 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

Ok to start U (gravitational potential energy) = m*g*h (mass , acceleration of gravity, and height) A) m = 66 kg , one bar = 155 food calories, 1 food calorie = 4186 J (assuming Joules for energy no unit was given) and g = 9.8 m/(s^2) so to start there is 155 FC * 4186 J = 648830 J to work off If he must work off those joules only changing U, then 648830 = m*g*h we have m, g, and U so we solve for h. h = 648830 / (m*g) --> h = 1003.138528 meters high they have to climb B) now there is some kinetic energy that subtracts from our U we are going to use K (kinetic energy) = 22 FC (food calories) * 4186 J = 92092 J So our new working U is -----> U1(from a) - K = 648830 J - 92092 J = 55673 J our new equation for height uses this new U U = m*g*h ------> 55673 J = 66 kg * 9.8 * h ----> h = U/(m*g) ----> h= 860.7575758 meters high **note --> E (total energy) = K + U which is why we can subtract K from total to get new U Hope this helps.

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