Question

The food calorie, equal to 4186 J, is a measure of how much energy is released when the body metabolizes food. A certain fruit­and­cereal bar contains 140 food calories. (a) If a 65­kg hiker eats one bar, how high a mountain must he climb to "work off" the calories, assuming that all the food energy goes into increasing gravitational potential energy? (b) If, as is typical, only 20% of the food calories go into mechani- cal 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. Aperson's "metabolic efficiency" is the percentage of calories eatenthat are actually used; the rest are eliminated by the body.Metabolic efficiency varies considerably from person toperson.)

Answer 1

Our variables

`E_c = 4186J`

A bar contains 140 calories.

A) When you eat a bar you gain

`E= 140*4186J = 0.586*10^6` calories.

To climbing we use the equation of Potential Energy, that is,

`U= mgh`

That should be the equal energy gain when you eat a fruit&cereal bar

Therefore from,
`U = E`

We use the equation of Potential Energy to find the high.

`h= (E)/(mg) =(140x4186)/((65x9.8)) = 920m`

B. Only 20% of food energy is available.

Then,
`E x 0.20 = mgh'`

Then, Height,
`h' = h*20\%`

`h'=184m`