(a) Calculate the energy in kcal used by a 60-kg woman who does 54 deep knee bends in which her...

Question:

(a) Calculate the energy in kcal used by a 60-kg woman who does 54 deep knee bends in which her center of mass is lowered and raised 0.400 m. (She does work in both directions.) You may assume her efficiency is 20%.

(b) What is the average energy consumption rate in watts if she does this in 2.75 min?

Work Energy:

The energy consumed by the woman is equal to the work done against gravity in 54 bends. This energy has to be converted into units of Kilo calorie. The energy spent is the ratio of energy consumed and efficiency. The average power is the ratio of total energy spent by woman to the total time interval.

Answer and Explanation:

Given:

{eq}m=60\ kg \\ N=54 \\ h=0.4\ m \\ \eta =0.20 \\ t=2.75\ min {/eq}

a)

Energy consumed by woman, {eq}E=N(mgh) \\ E=54(60 \times 9.8 \times 0.4) \\ E=12700.8\ J \\ E=3.035\ kcal \\ {/eq}

Actual energy spent {eq}U= \dfrac{E}{\eta} \\ U= \dfrac{3.035}{0.2} \\ U=15.177\ kcal \\ {/eq}

b)

Average energy consumed, {eq}P= \dfrac{U}{t} \\ P= \dfrac{15.177 \times 4184 }{2.75 \times 60 } \\ P=384.86\ W {/eq}


Learn more about this topic:

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What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
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