Question

he 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 130 food calories per bar.

Part A If a 72.0 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? Express your answer in meters. h h = nothing   m   SubmitRequest Answer 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.)

Answer 1

Given data:

1 food calorie = 4186 Joules

Hiker consumes 130 food calories

Therefore energy acquired by hiker = 130 x 4186 = 544180 Joules

Answer Part A:

We know that formula for potential energy is given by. :

Where m is the mass of the body ( 72 kg in this case)

g is the acceleration due to gravity ( 9.8 m/s²)

h is the height above the ground

Given all the energy is converted into mechanical energy therefore energy acquired by hiker will be equal to potential energy.

Substituting values we get:

Which is the required height covered by the hiker.

Answer Part B:

Now only 25% of the food calories are converted into mechanical energy therefore the hiker will use only 25% of the energy in hiking . Which leads to:

This is the height covered by the hiker when only 25% of his calorie intake

is converted into mechanical energy.

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