After a 5-min workout on a Climb Max stair machine, the readout panel reports th

Question

After a 5-min workout on a Climb Max stair machine, the readout panel reports that the 72-kg user burned 19.7 Calories and climbed a total of 165 steps. The chemical potential energy in foods is measured in units called Calories (notice the capital C). This "food Calorie" is equal to 1000 calories. A) If each step is 20 cm in height, how much would the potential energy of the user have changed if she were actually climbing a stairway? B) What was her rate of change in potential energy? C) At what rate was her metabolism consuming energy? D) What is her efficiency in converting the energy in the chemical bonds in her food into potential energy?

Explanation / Answer

calories burned per step = a = 19.7*1000/165 = 119 C/step..........................A) change in potential energy = p = m*g*h......m- mass of user, g- acceleration due to gravity, h- height climbed.....p=72*9.8*(165*0.2) = 23284.8 J = 5355.5 C ....(J- Joules...1J=0.23 C).......B) time taken to climb stairs t = 5 min = 300 sec.......thus rate of change of potential energy = p/t=5355.5/300 = 17.85 C/sec.......C) rate of consumption of energy by metabolism = b = calories burned / time = 19.7*1000 / 300 = 65.6 C/sec.....D) efficiency of energy conversion = e = (potential energy/ calories burned)*100 =( 5355.5/ 19.7*1000)*100 = 27.1 % .......

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