We need to first think about some other things first. Think about a cube that is one foot along each edge. We call its volume one cubic foot and the area of any of its six surfaces one square foot.
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The area of each surface is two feet by two feet now, or FOUR square feet. The amount of space inside it (the volume) is two feet by two feet by two feet, or EIGHT cubic feet. If you don't follow that, think about how many of the smaller cubes would be necessary to make one of the bigger cube. A layer of them would have 4 smaller cubes and there would have to be two layers, or eight all together!
What in the world does this have to do with 12-foot tall people? (I'm getting to that!)
Even though we were just talking about cubes, somewhere in Geometry there's a proof that any shaped object could be duplicated by a whole bunch of tiny cubes. So, ANY shaped object would follow this rule, including the bodies of PEOPLE!
We happen to be made up of mostly water, so we weigh about the same as the same sized volume of water would. I happen to be about six feet tall and I weigh about 200 pounds, about normal for people of my height. Since water weighs about 64 pounds per cubic foot, I am sort of the equivalent to a little over 3 cubic feet of water!
Now, let's think about a big version of ME, that is the same shape (called the same proportion), but who is twice as tall, or 12 feet tall. He would also be twice as WIDE as me and twice as THICK. Otherwise he would look REALLY skinny! Remember that cube stuff. So, how does HIS volume compare to mine? Yup! Twice as tall, twice as wide, and twice as thick, means he has eight times the volume of me. Since he would also be made up of nearly all water (the same stuff as me), this means he would weigh EIGHT TIMES AS MUCH AS ME! Wow! I weigh 200, so he would weigh 1600 pounds!
Does this seem weird? It shouldn't. Let's think about something else for a moment. I weigh 200 and I'm 6 feet tall. If I was FIVE feet tall (and the same shape or proportion), how much would I weigh. Well, I would be 5/6 as tall and 5/6 as wide and 5/6 as thick. If you multiply these, you get 125/216. Multiplying my 200-pound weight by this would tell us how much I would weigh as a 5 foot tall person. If you do it, you'll get about 116 pounds. A lot of women that are 5 feet tall weigh that much!
We might as well go the other way. What if a person had my shape or proportion but was SEVEN feet tall, like a lot of basketball players? In this case we would multiply 7/6 by 7/6 by 7/6 which is 343/216. This would indicate a seven-foot-tall me would weigh about 317 pounds. You may have noticed that they tell the players' weights when they introduce them before a game, and often the seven-foot-tall players weigh between 280 and 320 pounds. Of course, they may be a little more in athletic shape than I am, but it's still close!
OK. So we've established that the 12-foot tall me would weigh about 1,600 pounds. Is that possible?
We need to go back to our cubes for a moment. And think about a rope. What if a rope is twice as big as another rope. How much stronger would it be, if both were made of the same stuff? Our cubes give us a clue. The rope is twice as thick in one direction and twice as thick in another direction. If you CUT the rope, you would therefore see FOUR times the area of rope (sort of like the area of the surface of our cubes). Why is this important?
My thigh (leg) bone is about one inch by one inch thick near its middle. The big guy would have that bone twice as wide and twice as thick, or having FOUR times the area of MY leg bone. If he weighed FOUR times as much as me, his leg bones would be fine for him. But, remember, he doesn't weigh FOUR times as much as me, he weighs EIGHT times as much. In other words, every tiny little bone cell in HIS leg has twice as much load on it compared to the same bone cell in me.
You know how sometimes people break their legs in accidents? Well, he would be a LOT more likely to break his leg bones (and other bones as well).
Getting back to my rope example above: All of your muscles are sort of like ropes. They pull when your brain tells them to. Stronger muscles are thicker. Body builders make their bicep (arm) muscles really strong, and so they get thicker and the person has bigger biceps.
How much does your arm weigh? Even your doctor probably doesn't know the answer to THAT question! Can you think of a way to find out what it weighs? There are actually a bunch of approximate ways, but one of my favorites depends on that fact that our bodies weigh about the same as water. Imagine filling a (clean) plastic garbage can with water. OUTDOORS! To the very top. The stick your arm all the way in. As you do this, some water will be DISPLACED and will spill over the edge of the garbage can. You could try to catch all of that displaced water. OR, after you remove your arm from the water, the level will be lower. If you then borrow mom's measuring cup, you can measure and pour more water into the garbage can to fill it up again.
In either case, the amount of water you measure has the exact same volume as your arm! In my case, it's about 15 pints. A pint of water weighs about one pound, so my (whole) arm weighs about 15 pounds.
Getting back to the big guy. How much would HIS arm weigh? Yup! Eight times what MY arm weighs or about 120 pounds. But his arm and shoulder MUSCLES are only FOUR times as strong as mine because they are only four times the area of mine. What does this mean?
His arm would seem to him to be twice as heavy as my arm feels to me. I could duplicate that effect by attaching two bricks (about 15 pounds) to my arm. Can you see how hard it would be to raise my arm if I had the extra weight of bricks attached to it? And how much slower I would do it? Do you think I could throw a football or baseball if I had bricks attached to my arm? Not very well!
Everything about the big guy makes the problem worse. His lungs work by the area of lung surface that touches the air that he breathes in. That is an AREA, so his lungs would have four times the capacity of my lungs. But, he has EIGHT times as much blood (VOLUME) and amount of cells that need oxygen that has to be supplied by the lungs. That means that he would always feel out of breath, and even a little exertion would overload his lungs and he would start gasping and wheezing! Ever see THAT in a cartoon big guy???
There are hundreds of different subjects we could think about related to features of the 12-foot-tall guy. They all strongly show that he would be very weak and slow. He would have to eat eight times as much food as me, but the area of his intestine would only be four times as big, so his digestive system would have to spend twice as much time processing the food he ate! Stuff like that.
SO!!! If a 12-foot-tall person will ever exist, he will certainly be very weak and slow, and I don't see how he would even survive unless his parents almost continuously took care of him, because in many ways, he would not be able to take care of himself.
If you also consider these ideas regarding very SMALL creatures, you can now understand how mosquitoes can have such skinny legs! For SMALL creatures, the AREA gets smaller slower than the VOLUME or WEIGHT does. That means that things like WINGS can work GREAT for tiny critters, while they become more useless as the size of the creature becomes larger. This explains why most birds and other flying or soaring animals are fairly small.
Now do the same where all the dimensions are doubled. The bucket now contains 5 * 2 * 2 * 2 or 40 gallons of water and it weighs 320 pounds. The sticks (legs) are now four feet tall and they are 1" in diameter. This is like a very tall kitchen table with really skinny legs! Do you see that such a tall table, with skinny legs and with 320 pounds on top of it would have somewhat wobbly legs? And if any one leg collapses, so does the whole table?
You could take this one step farther, doubling it again. Now we would have a weight of 2560 pounds (about as much as a car) sitting eight feet above the ground on just four 2" diameter sticks! If you did it extremely carefully, you might get such a car to stay there for a moment, but if even the wind pushed against any of the "legs" everything would collapse.
And, going the other way, at half the dimensions, the bucket would hold five pounds (about half a gallon, a two liter pop container) and the sticks would be one foot long and about the diameter of pencils. This would be very strong, and you could easily add quite a bit of your weight on it before the sticks broke.
These examples use the exact same logic described above, but instead of animals, they use common things we know about, to try to confirm what is said above.
This logical approach also has many implications when we consider the VERY largest of the extinct dinosaurs. I have created a Sauropod Dinosaur Physics Subjects that discusses a number of these size-related subjects.
This is the case primarily because no one (and no textbook) showed them the incredible usefulness a moderate knowledge of Physics can be.
This series of lessons is meant to correct that situation. Students in High School or College Physics should be able to benefit from and EVEN ENJOY (!!) these Physics lessons. The lessons should help clarify the usages of a lot of those dry subjects and equations the teacher or professor tries to ram down your throat. These lessons are freely made available to teachers and professors for use as they desire, either on the InterNet or in the classroom.
(The preceding paragraphs appears in each lesson, in the event that someone happens to find a single lesson from this series as a result of a search-engine search.)
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago