If a 75.0kg hiker eats one of these bars, how high a mountain must he climb to \
ID: 1698731 • Letter: I
Question
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?
If, as is typical, only 23.0% 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
Amount of energy gained by the personfter eating one bar is W = 160 food cal = (160)(4186 J) = 669760 J Here only 23.0 % of energy is utilized as mechanical energy. Mass (m) of the peson = 75.0 kg Acceleration due to gravity is g = 9.8 m/s^2 As we know the formula for the potential energy is W = mgh h = 0.23W / (mg) = 209.6 m