Let's assume Short Person is 5 feet tall and the Normal Person is 5 feet and 8 inches tall.
Let's assume the uphill hike has steps with 1 foot height.
How much more work or energy does this require of the shorter person due to shorter legs?
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2 Answers
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The gain in potential energy is $mgh$ and the CM of each person rises the same amount, so if they weigh the same and are equally efficient, it takes the same amount of energy for each.
answered Mar 18, 2016 at 2:58
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$\begingroup$ The OP specifically wants to know about the case where someone has shorter legs which means you can't make the assumption that they are equally efficient. Although the OP didn't specify weight, it's unreasonable to assume equal weight as well. $\endgroup$– JBentleyCommented Mar 18, 2016 at 9:49
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$\begingroup$ @JBentley: It is important to think about a question and what you are interested in. $\endgroup$ Commented Mar 18, 2016 at 14:42
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$\begingroup$ Let's assume short person is 110 lbs and taller person is 150 lbs. $\endgroup$– RebecaCommented Mar 19, 2016 at 22:16
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$\begingroup$ The physics answer is that the taller person needs a factor $\frac {40}{110}$ more energy to get up the hill. It seems reasonable that the efficiency of converting food to mechanical work should not be too different depending on height. The shorter person will need more steps, but each step will represent less energy output, so shorter legs are no disadvantage in this regard. $\endgroup$ Commented Mar 20, 2016 at 4:11
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The work done is same as Ross Millikan answered. However, it can be more stressful for the shorter height because, climbing one foot stair may be harder for the shorter person because, the muscle use is more out of range as compared to a taller person. So, there may be a difference in the "spent energy" due to some work less movement of the muscles by the short person.
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$\begingroup$ That's what I want to somehow quantify. $\endgroup$– RebecaCommented Mar 18, 2016 at 5:49
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$\begingroup$ Quantification will involve number of parameters and math. May be someone else can do that. I do not think I can. In any case it is not likely to be very accurate. $\endgroup$– kpvCommented Mar 18, 2016 at 5:57
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$\begingroup$ Could this quantification be done experimentally? What would be the difficulties in setting up such an experiment? $\endgroup$ Commented Mar 18, 2016 at 7:19
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1$\begingroup$ @FreezingFire: It would involve very many difficult parameters - like body structure, proportional growth, muscle distribution etc. Height is just one parameter. Even two people with same height may end up spending different amount of energy depending upon these other factors. I would not spend much time on quantifying it based upon height alone. It would be a complex and imperfect quantification in my opinion anyway. $\endgroup$– kpvCommented Mar 18, 2016 at 18:00