A 51 kg woman cheats on her diet and eats a 619 Calorie (540 kcal) jelly donut f

Question

A 51 kg woman cheats on her diet and eats a 619 Calorie (540 kcal) jelly donut for breakfast.

(a) How many joules of energy are the equivalent of one jelly doughnut?


(b) How many stairs must the woman climb to perform an amount of mechanical work equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 cm.

(c) If the human body is only 26% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?

Explanation / Answer

mass of the woman m = 66 kg energy equivalent of the doughnut E = 475 kcal                                                         = 475*103 cal .................................................................................... a) energy equivalent of  one jelly doughnut in joules is               E = (475*103 cal)(4.186 J / 1 cal)                  = 1988.35*103 J                  = 1.988*106 J b) the height of a single stair h = 15 cm                                           = 0.15 m work done E = N(mgh) number of stairs N = work done / mgh                             = (1.988*106 J) / (66 kg)(9.8 m/s2)(0.15 m)                             = 20490.62 stairs                             = 2.049*104 stairs                             = 2.049*104 stairs c) mechnical energy E ' = 20 % of E                                  = 0.2 E mechnical energy   E ' = N'(mgh)                                         N' = E' / mgh                                   = (0.2 E) / (mgh)                                   = (0.2)[E / mgh]                                   = (0.2)N                                        = (0.2)(20490.62)                                  = 4098.12 stairs
                                  = 4.098*103 stairs

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