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When we walk, is the magnitude of the earth's force on us greater than if we were standing still?

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up vote 5 down vote accepted

It bobs around as you go through your stride, but it's greater on average.

Newton's second law, F = ma, tells us that Earth exerts more or less force on you depending on whether you are accelerating. When you're walking, you oscillate up and down. If you're accelerating up (which happens when your body is at the lower parts of your gait), the Earth exerts more force on you. If you're accelerating down, it exerts less. The average vertical force is the same as if you were standing still.

That accounts for vertical forces. There are also some horizontal forces from the Earth, but these are generally small unless you're starting/stopping very abruptly. Since they're perpendicular to the normal force Earth exerts on you, they always increase the total force. As you walk, the horizontal (i.e. friction) force from Earth on you will change directions, depending if you're momentarily speeding up or slowing down. If you could walk very smoothly, you could minimize these forces.

One way that you could have the Earth exert less force on you on average while walking would be to walk in the direction of a strong wind. When you're standing still in a strong wind, the Earth exerts a friction force to keep you steady. But if you walk with the wind, its apparent strength is decreased, and the frictional force needed to keep you from sliding away can go down.

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ok. Thank you! :) – Jeeter Jan 3 '13 at 22:21
Isn't this basically the same as ? If so, that suggests the average force would be the same as when you're standing still. – John Rennie Jan 4 '13 at 9:50
@JohnRennie I think my answer is pretty clear when it says "The average vertical force is the same as if you were standing still." The total force is greater on average because if you are standing still and there's no wind, there's no horizontal force on you, but there is when you're walking. – Mark Eichenlaub Jan 4 '13 at 11:25
@MarkEichenlaub: oops, yes, of course, I'd forgotten there would be a horizontal component to the force. Actually that means my answer to the bridge question is wrong, or at least incomplete, since I didn't include the horizontal force. – John Rennie Jan 4 '13 at 13:22
@JohnRennie Cool. Well, I think for the bridge they were really focusing on the vertical component as being tricky. – Mark Eichenlaub Jan 4 '13 at 17:04

Just to quantify Mark Eichenlaub's answer, the typical profile of the ground reaction force while walking looks something like the following image taken from here:

enter image description here

Vertical (red) and horizontal (blue) forces are for a single leg. Because there is simultaneous contact of both feet during walking, the actual total vertical force of the ground on the body looks like this graph taken from here:

enter image description here

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Thanks for the plots! – Mark Eichenlaub Jan 3 '13 at 22:57

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