Is atom size a limiting factor in construction?

Factual Questions
1

This is something that has bugged me for the better part of 15 years and I have never been able to get an answer for it. Its probably a really stupid question, but here goes:

Does the size of atoms prohibit how large things (buildings, people, toys, planets, etc.) can be? Let me explain:

I’ve always wondered why toy cars were so resistant to damage while an actual car would dent when even a shopping cart was driven into it with little force. At first I thought: its probably because the proportions arent right. Suppose a toy car was 1/1000 of a real car, then the millimeter thick metal on a toy car would have to be 1 meter thick on a real car, thats why toys are so resilient. Is that the case? If so, how thick would car door have to be so that you could run into a wall at 60mpg and not have the car be damaged?

Ok, so maybe thats the answer, but it doesnt apply to other things. For example, if its simply a matter of proportion, why is it that tiny animals like ants, beetles, and spiders can lift many times their own weight, while a human many magnitudes larger does not have proportional strength? How is it we’re constructed so weakly compared to an ant? And if we had giant ants, could they lift up a car? I realize that goes into a lot of speculation and there may be no answer, but there’s more

On the same biology question, why are larger things (generally) slower? I think the world’s faster creature (in proportion to his body weight) is a beetle. If it were man sized, it would go 0-100 feet in like 1 second. Why does it seem like larger animals get the shaft on superman-like abilities? If a beetle’s tiny size and tiny amount of energy required allows some mass/energy function to give it super speed, why arent elephants built the same way (ie. why arent elephants eating the same amount of energy proportional to a beetle and able to zip around at breakneck speeds?)

Another thing is human construction. The larger things are, the more fragile they seem. Think of it like jenga blocks. A small thing like that can be taken apart, put back, thrown on the ground, abused, with little change in its status. However, a tree trunk seems mighty fragile compared to a jenga block. If you dropped it from a hundred feet in the air, it would break and splinter. Why? Isnt it also wood? If its a hundred times bigger, shouldnt it be a hundred times stronger?

One more example (sorry that this is getting lengthy) is in construction. Why is there a limit on how tall or big something can be made? Is it simply because of lack of construction materials that makes it impossible to build a building 10 times the size of the Sears Tower? I mean, to a proportionally tiny creature, a Barbie dreamhouse would be 100 or 1000 stories tall right? Whats to stop people from making a 1000 story tall building if to ants, such things are already astronomical?

I guess all these examples are just my way of asking if there is some physics reason that things have set limits the way they have, like something to do with how strong atomic bonds are or something. Please help! :confused:

2

Yes, there is a physical reason for what you observe. No, it has nothing to do with the size of the atom. The real reason is best explained by an engineer. Sorry, I’m no help there.

3

One of the classic essays on the subject is On Being the Right Size by J. B. S. Haldane.

4

One thing to consider is that volume increase by the cube of the size. In other words, if you have toothpick, and you scale it up to be the size of a telephone pole (lets say, 1000x) than it’s volume (and mass) increases by a billion times. So large objects can’t be built the way small ones can.

5

I would think it would only really apply in the other direction - at some point as we work at constructing more and more complex machines in smaller and smaller sizes, at some point we will reach the ‘limiting factor’ of having building blocks of only a certain size, (and temperamental ones in certain ways, what with potential nuclear instability and quantum indeterminancy,) that will keep up from miniaturizing any more.

Not the same for large structures. You could probably construct a non-atomic model of the world, in which everything was infinitely divisble, and as long as these non-atomic substances had similar structural strength to the atomic matter we know, they’d still be vulnerable to the square-cube effect as I understand it.

6

It’s called the Square-cube law, and it’s the primary reason why small things are different from big things. It’s not related to the fact that matter is atomic though.

7

Square Cube law, taken further:

Let’s take an ant and blow it up 1,000 times in size (1,000 times its height, 1,000 times its width, 1,000 times its length). Let’s say the ant weighed 1mg. If you were unaware of the square cube law, you might multiply a milligram by 1,000. But, it’s not going to weigh a gram — It’s going to weigh 1000 kilos (over 2,200 lbs)! It’ll be a lot harder for that ant to lift 100 times its own weight, now.

8

Another point about scaling: As a rough rule of thumb, all animals can jump about the same height, regardless of the animal’s size. The energy you can get out of your muscles is roughly proportional to the volume of the muscles, which is likewise proportional to mass (all living things are close to the same density). Meanwhile, gravitational potential energy is the product of mass, height, and the gravitational field. So if you double a creature’s size, you octuple its muscle energy, but you also octuple its mass, so that energy takes it to the same height. Hence why a human and a flea can both jump up a few feet.

9

It occurs to me that an object made from smaller atoms would probably both have stronger atomic & molecular bonds ( less distance between the electrons and other electrons, and between electrons and the nuclei ), and be denser. I’m not sure how that would balance out though.

10

I don’t know about mechanical limits (which is what your question is about), but an important practical limit for the size of building is elevators. At some point, most of the space in the building would have to be used just to move people around.

11

As far as living things are concerned, on limiting factor is the surface/volume ratio. Since volume scales with the cube of the dimension and surface scales with the square, large animals have relatively less skin than the smaller ones. For example, a cube of 1 cm has 6 square cm of surface for one cubic cm, whereas a cube of 10 cm has 600 square cm for 1000 cubic cm.

This is a problem for animals since the skin allows to release heat produced by metabolism. The amount of heat produced is proportional to mass*metabolism, and the amount of heat released is proportional to the surface. Therefore, an elephant must have a slower metabolism than an ant otherwise it would overheat.

Another point is that the small animals with a high metabolism tend also have a shorter life span. So they don’ have the time to get as big as an elephant !

12

Isn’t it quite obvious? How much pressure can a square foot or square meter of foundation material stand without crushing? That’s the limit of the weight you can put on top of it.

The issue here is that if you enlarge the dimensions of an object by a factor X the surfaces enlarge by X^2 and the volumes and masses enlarge by X^3. So, masses grow more than surfaces and surfaces are required to sustain proportionally more pressures and tensions.

Take a horse and enlarge it to twice the size. The mass has grown by 8 but the sections of the tendons and bones has grown by 4 so now they are supporting twice the effort. You need to redesign that horse with thicker bones , tendons, etc… and you have an elephant.

As you can see you can’t get much bigger. There are no legs which a whale could use.

Take a bird. If you make it twice the size you make it 8 times as heavy but the wing area is only twice so a bigger bird needs proportionally larger wings. Inversely, an insect can fly very easily even if the wings are not too efficient.

Same thing with making objects withstand shock. The smaller the size the less stress per area of material.