Center of Mass Question

1. Oct 23, 2005

kamui8899

I came across a particular result which bothered me, it stated that: Result: A person bending to 90 degrees at the waist with their back to a cliff will fall because their center of mass is past their feet.

This statement perturbed me, because, when I applied it myself, I found that, while I did fall, my muscles were tensing before I fell. Thus, if my muscles were strong enough would I have been able to prevent myself from falling?

One of my friends tried to apply the laws of levers and fulcrums to this problem, claiming that gravity acted as a torque around the fulcrum of your feet, and that there was no way to stop yourself from falling without applying some external force, like throwing a rock.

However, this may be true but it doesn't seem to explain the case where a greater mass is off the cliff, being held up by sufficient muscular strength by a lighter mass on the cliff. That is to say, if I were holding 300 pounds of weight in my sufficiently strong arms straight out from my body, I would fall forward, regardless of the upward force I exert on the weight with my arms. This seems incorrect, because I believe that the upward force exerted by the arms, generates a reciprocal force that pushes your feet down onto the ground, thus this force allows you to stay on the ground rather then fall, regardless of the fact that a greater amount of mass is off the cliff (the heavy rock) then on the cliff (the man holding the rock).

If something came across as unclear, feel free to ask for a further explanation of the problem.

If anyone can shed any light on this matter I’d be most appreciative. Thanks.

2. Oct 23, 2005

Galileo

Unless you are able to exert a torque about your feet in the opposite direction as gravity does you will fall. Ofcourse your feet are not points and if you have really big feet you may be able to do it. It doesn't seem likely though.
Also, if you bend over you have the tendency to put your butt backwards to keep your center of gravity above your feet.
Stand with your butt against a wall and bend over 90 deg. You'll definately fall.

What we have here is what physicist call a 'couple'. If you hold a 300 pound rock in front of you with outstretched arms, gravity will act on the rock downwards and you hold it up with your arms, so the net force is zero. But the two forces do not act at the same points. The gravitational force on the rock acts in the rock's center of gravity. The force you exert upwards acts at the point where your feet touch the ground. So there will be a torque on you.

BTW: You didn't really believe you could carry a 300 pound stone in front of you and NOT topple forward, did you?

3. Oct 23, 2005

kamui8899

Can you specify the direction of the torque you indicated occured in the second part of your explanation, I'm assuming you mean that the person holding the rock will fall off the cliff due to this torque. Essentially then, there is no way to prevent the person holding the rock from falling by enhancing the person's strength to any degree.

Also, you mentioned the fact that your feet aren't points on the ground and that the larger your foot, the easier it would be to hold yourself in position, why is this so? Does it change the center of gravity, approximately how big must your feet be to retain your posture? How exactly do your feet compensate for torque?

Thanks for the insight.

4. Oct 24, 2005

Galileo

Let me answer the second question first. Having large feet doesn't change your center of gravity (much. Unless they're really heavy I guess). Imagine you have huge feet or wearing long clown shoes. Then your area of support is much larger and if it's large enough your center of gravity will be above your area of support. If we assume you are strong enough to hold your body stiff we can treat you as a rigid object. If you are to topple you will naturally do so about a point at the edge of your area of support. So if your center of gravity is 'outside' this area (that is, not exactly above it) you will fall. Otherwise you will be stable. A single picture will speak for a thousand words, but I can't seem to find a good one...

About the first question: No indeed. No amount of strength will help you from falling over. Strength will help you retain your poise instead of crumbling like a cookie under the weight of 300 pounds. To make it simple, just take a statue. A strong, rigid unbreakable statue of a guy with outstretched arms. (A person's strength would amount to the unbendability of the statue). Put a heavy block in his arms. If this added mass shifts the center of gravity outside is area of support it will fall. Incidentally, that's why it's useful to have a large pedestal.