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The ​food calorie, ​equal to 4186 J, is a measure of how much energy is released when the body metabolizes food. A certain energy bar contains 140 food calories. a) If a 65-kg 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 more typical, only 20% of the food calories go into mechanical energy, what would the answer be to part (a)?

Answer :

MechEngineer

Answer:

a) 919 m

b) 183.8 m

Explanation:

140 calories = 140 * 4186 J/calorie = 586040 J

a)When the hiker climbs a mountain, this energy is converted to potential energy, which has the following formula

[tex]P = mgh[/tex]

where m = 65 kg is the mass, g = 9.81 m/s2 is the gravitational acceleration and h is the height that he climbs

[tex]586040 = 65*9.81h[/tex]

[tex]h = 586040 / (65*9.81) = 919 m[/tex]

b) If only 20% of food energy goes into mechanical energy, then the actual potential energy is

586040 * 0.2 = 117208

Similarly, the height that he could climbs is

[tex]h = 117208 / (65*9.81) = 183.8 m[/tex]

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