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I have a silly bet with a friend of mine.

One of us argues that walking up a hill whilst leaning forward requires less exertion, due to your centre of mass being further forward, and therefore gravity would assist and less muscle energy would thus be required to climb the hill.

The other of us argues that this cannot possibly be true, as the amount of work required to climb the hill is the same regardless.

I know this all sounds ridiculous but we'd really like to settle it!

TIA!

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    $\begingroup$ If you define "climbing the hill" as the first body part that touches the finish point then leaning forward would be more efficient as when you are two paces away you can simply collapse forwards saving yourself two paces $\endgroup$
    – Tom Gullen
    Sep 19, 2011 at 15:42
  • $\begingroup$ "leaning forward" is mostly subjective. When walking, thare is not more leaning forwards than when standing still, when running one thinks one would lean forward, but this is wrong. You always have Your center of gravity above the area where Your feet make contact with the ground. Air resistance would cause some leaning forward, but it is much too small. You lean forward in the moment, when You accelerate from rest, but not during walk/run. $\endgroup$
    – Georg
    Sep 19, 2011 at 16:33

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Mechanically speaking, both strategies are equaln efforts. (maybe there is an anatomical difference in energy efficiency, depending on your posture and what muscles you use, but I assume the question is purely mechanical)

Gravity won't help you, when leaning forward: you could use it shortly, to move a bit further on the road, but you pay the price in potential energy: you would be falling, and therefor have to bring your center of mass back up again.

Actually, when walking, you hardly have anything to choose on your position of center of mass. Given a certain walking speed, one has to lean forward a certain amount to avoid falling.

This reminds of the joke with bike with a smaller front wheel, so that every road is downhill ;-)

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Does leaning forwards change the amount of gravitational potential energy gained when walking up the hill?

Of course not - it's still your mass × g × the height of the hill. Hence, it can't make any difference to the amount of work needed.

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