Friday, February 22, 2013

Why don't they flip?

You have seen them in DC, Philadelphia, Vancouver or other places around the world - cool sculptures that seem out of balance; sculptures that appear on the verge of falling yet are perfectly stable.
How is it possible?
I know this is not really math but semi-related.

HaBima square, Israel

Laguna Beach, CA, USA



Philadelphia, PA, USA

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.


thelittlebird said...

The weight of the sculpture is distributed so that even though there is not visual balance, their is balance of mass. This would most likely be achieved by using denser material in some parts of the sculpture and less dense or even hollowed materials in others.

What's going on with that Norway statue?! I think I had a dream like that once!!

TyYann said...

Most likely, they are strongly anchored in the ground.

katrina said...

They are cantilevered - the weight is balanced heavier on the bottom/base vs. The extended part.

Annie said...

I'm not sure of the exact method from a construction point of view but they must make the base of the statues strong and heavy to create a low center of gravity to offset the (seemingly) top heavy and off center top of the structures.

anne-marie said...

In these cases, there is no motion or action so
the object will stay in balance if its center of gravity is above its base of support. If the center of gravity is not above the base of
support, the upward support force from the
base is not anymore aligned with the downward force of gravity and it creates a torque that rotates the object such that the object won't be balanced anymore. The base of
support is the entire area that surrounds all
the points of contact.

Anonymous said...

These statues do not fall because of the relation of the statues to their base of support. the weight of the object and gravity. All these objects have quite a bit of weight. The upward support force from the
base is aligned with the downward force of gravity. The hardest one for me to fathom is the first one with the 3 stacking balls. It looks like the top ball may not even be in a line with part of the bottom ball but that might not be true because of the way the picture is taken Also, it makes a difference if the statues are free standing and not anchored into the earth. I tried the standing poses myself and I was not too out of balance getting into them because the arms counterbalanced my body so the line of gravity shifted to a point aa few inches behind my back. It would seem to me that the balls have to be anchored to make them not fall over. It would be like the glass bridge over the Grand Canyon.However, maybe the top ball is over the bottom ball in real life and I cannot tell by the picture. The guy running away is somewhat held aloft by his leg up in the air and the other guy and the manhole anchoring him so the center of gravity is shifted between the two men.



Leah said...

It seems to me that there must be some kind of below-level, foundational armature. If it is heavy enough, or extends underneath the sculpture in the correct direction, it will allow the balancing of an apparently off-center sculpture. I love those examples above!

Anonymous said...

It's all about center of gravity. All sculptures are designed to keep the center of gravity at the bottom.

Jerome said...

Until I saw these pictures I thought the only way to do these center of gravity illusions was something like the last photo in the following reference.

That is the center of mass is actually in line with the balance point, and the ends of the two forks provide a mass that counterbalances the tines of the front end of the forks. There are various toys that work the same way.

These sculptures must work on a slightly altered principle. I think, but I'm not certain, that the key to what is going on has something to do with the picture of the three disks in HaBima Square in Israel. I would guess that the base is made of something much heavier than the other two disks. The top two might be hollow or filled with cork (to prevent people from walking up to the middle disk and tapping it to test for an echo).

The sculpture from Norway could be explained by density differences. Perhaps the right side (our right) is made of something quite a bit heavier than the part of the sculpture on the left.

I consider the two from Philadelphia and England impossible to explain. That's OK with me. Mystery and magic are wonderful and always to be treasured when found.

Jerome Cherry's wife said...

All of these spectacular sculptures are top heavy, meaning that the mass of weight of each of them is exactly at the position where they should topple over, but they don't. The only thing that can counter balance their supposed unbalanced state is that they may have a wide base or the base is of sufficient weight to balance the unbalanced state, coupled with the fact that each has a strong armature to bend them into precarious looking unbalanced anomalies. Two of them, the one from Israel and the one from Philadelphia must have their supporting/balancing base below ground level.

Jerome said...

I forgot the California statue. I can see it's center of gravity and the material in the right leg and hips being of a different material.

Anonymous said...

I think these sculptures don't fall over because of two factors:
(1) the center of gravity of the sculptures isn't that far horizontally (x-direction) from the base. For example, if one of the sculptures had a small base section and a very large, heavy head that was far horizontally from the base it would be more likely to topple.
(2) a strong internal structure (rods or other) and mounting system to the ground to keep the sculptures in place and upright.


Maria said...

Very interesting answers. I am thrilled to see that some of you actually tried imitating the sculptures to check the balance! Many of you seem to remember much more from the high school physics than I do. I assume that these peculiar sculptures have a heavy underground base that keeps their center of gravity (center of mass)above their base.

If I find out more I will share with you.
A puzzle point for each of you.

This reminded me about the home renovation project we are considering, where the whole old and steep staircase we have must be destroyed and replace without tipping over the whole house...

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