Question

The food calorie, equal to 4186J , 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.If a 69.0kg 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 20.0% of the food calories go into mechanical energy, what would be the answer to part (a)?

Answer 1

The hiker will go up to 850 m on the hill

Explanation:

The total energy gained  by the hiker = 140 x 4186 J

This energy is consumed in the potential energy acquired , while climbing up the hill.

The potential energy P.E = mass of hiker x acceleration due to gravity x height

Thus

140 x 4186 = 69 x 10 x h

or h = $\frac{4186x140}{69x10}$  = 850 m

If the 20% of the total energy is used

the height h₀ = $\frac{0.2x4186x140}{69x10}$ = 170 m