Question

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 1

a) 919 m

b) 183.8 m

Step-by-step 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

`P = mgh`

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

`586040 = 65*9.81h`

`h = 586040 / (65*9.81) = 919 m`

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

`h = 117208 / (65*9.81) = 183.8 m`