Just finished watching Honey, I Shrunk the Kids with my 6 yo daughter. Fun movie, and really gets you thinking how it’d REALLY be if you were that small.*
So, let’s say one were shrunk down to less than an eighth inch [3mm] tall (the movie says a quarter inch [6mm] but i’m not buying it). I could say right off the bat that they would almost seem weightless, but by how much? What would the physics be like for a human adapted to 1g acceleration? What else am I not thinking of.
*Mods: feel free to move this to Cafe Society if that is where this belongs
I’m no physicist, but it seems to me that physics would work exactly the same for them, and they would feel no heavier or lighter than they felt when they were full size.
The main determinant of how gravity feels on earth is determined by the size of the earth itself. The planet is so large compared to any living creature that changing the size and mass of a creature, even by a factor of a hundred or a thousand, shold make no perceptible difference to how that person experiences gravity.
If there’s something i’ve failed to take into account here, i’m sure someone will correct me soon enough.
I was under the impression that if our mass were greatly reduced, that would in turn effect our weight on earth (to say, maybe less than a gram in this case?). Also, inertia wouldn’t have the same hold that it has on us now.
Sure, your weight would be much less, and if a real-sized person were to try and pick you up they would certainly notice the difference. But i’m not sure that you would actually feel any different, because your weight would still be in the same proportion to your mass, to your size.
It is also true that your inertia would reduced, because inertia, if i remember correctly, is mass x velocity. But, again, this would probably feel the same to you. That is, if running at full speed required 3 times your body length to stop when you’re full sized, then running at full speed would probably also require three times your body length to stop when you’re half an inch tall.
It’s possible that i’m not quite grasping the concept of your question. I’m sure someone will be along soon who can explain it better than me.
One thing that might be relevant to bring up here is the square-cube effect. A number of effects to do with mass and strength don’t hold up under expansions or contractions of scale because of this. (For instance, you can build a small model and have it be quite sturdy, build a full scale building or bridge or whatever out of the same materials, and it falls apart under its weight)
The basic principle is that mass is dependent on volume for structures of similar a constant composition, and thus if you shrink something down by half, you’ll reduce its mass to one-eighth. However. strength (structural and muscular strength) generally varies with cross-sectional area, and thus the total strength will only be down to one-quarter. The strength to mass ratio has suddenly doubled. If you shrink a five foot tall teenager (guessing) down to a quarter of an inch, that’s a reduction in height to 1/240th and thus the strength to mass ratio should increase by 240 times. I would think that they might notice that while running or jumping, that their bodies seem ‘lighter’ than normal because their muscle power hasn’t been reduced as much as their weight.
IIRC, this effect is part of the explanation for why ants are able to lift so many times their weight… they’ve developed strong muscles for their size, and their weight really just isn’t that much.
Not quite sure how any of this affects terminal velocity myself… think that mass and cross-sectional area are variables in that too tho.
Of course, all of this is assuming that the beam was able to reconstitute them with 1/13,000,000th (approx) of their former mass, and (presumably) that it was able to do it by mapping the structure of their bodies into a corresponding fraction of the atoms that made it up. If the beam just compressed their atoms into a much smaller space, they’d still have their full mass, and if it somehow ‘shrunk’ the individual atoms so that they’re each 1 thirteen millionth less massive… then I suspect all bets are off, because something so far out as that might mean that a lot of our other assumptions about how matter would behave are out the window.
What everybody’s forgetting is that a gentle breeze from an 8" tabletop fan would be like an 80 MPH wind when that fan is suddenly 64 times bigger than you.
You’d get blown around a lot. As you trek across the kitchen table and you pass in front of the air vent…now so high up in the ceiling you can barely see it…you’d get blown onto the floor.
In fact, in the movie, the dad remarks that the beam works by reducing all the “empty space” that exists between the fundamental particles, and leaving the particles themselves intact. I had to dismiss this, because i thought it seemed like a good idea at first, but obviously, now you’re just messing with the way the universe is set up to work, and that might change the matter that makes up their bodies in a fundamental and unknown way. Not to mention, if nothing else happened, they would retain their original mass and collapse under their own weight at that size.
…It’s good for the imagination to suspend the ol’ disbelief once in a while, but there’s only so far we can take this before it quickly becomes pretty ridiculous. Full sized man, call him 95 kg, typical surface area of the feet equal, uh, 300 mm x 80 mm x 2 each equals, uh, about 1980 kg per square meter, or about 19.4 MPa. Is that right?.
Anyhow, the point is this: reduce the individual dimensions down by a straight zoom factor of, say 240x each, and the floor load goes up by a factor of 240 SQUARED. Which is to say, the floor better be pretty strong. Getting across the soil in that garden, however, is going to be darned difficult.
Oh, wait. It’s a movie. Oh, well, that’s all right then.
Let’s make the following assumptions: Mass is conserved under shrinking, the kid’s feet are rectangluar and 6 inches by 3 inches. Suppose the kid is 100 pounds. The pressure the kid exerts on the ground is 100/(2 * 3 inches * 6 inches) is 2.777 pounds per square inch.
Under the shrinking ray, a 5 foot (60 inch) tall kid is mapped to a 1/8 inch tall kid. This is a scaling of 1/480 in each dimension, so now the kid’s foot is .0125 inches by .00625 inches, so that his pressure on the ground is now 100/(2 * .0125 inches *.00625) =640,000 pounds per square inch. I don’t think most surfaces can support this pressure. My guess is that they’d leave pretty deep foot prints and get stuck in the ground.
Make it even simpler. If you stick a piece of rebar upright in your garden and put your full weight on it, the rebar will sink quite easily into the soil. The footprints of the characters would be much smaller than the end of that rebar, so they’d sink even more easily.
But let’s assume that their mass is also scaled in such a way that this isn’t a problem. Running and jumping would still be radically different, unless their time sense is scaled as well. Consider that a typical person can easily jump over an obstacle which is, say, a third of the person’s height. For a person of normal height (180 cm), this would take about .7 seconds, from leaving the ground to landing again. If we’re supposing that our shrunken people run and jump in the same manner as we, then a shrunk must also be able to jump over an obstacle a third its height, or in this case, 2 mm. But this is a much lower jump; by my calculations it’d only take .04 seconds from launch to landing.
Nope you forgot to multiply by gravity and converted to MPa wrong. Using 10 m/s^2 (its closer to 9.81 but I am too lazy to get a calculator) thats 19,800 N/m^2 which is .198 MPa.
I may be wrong, but seem to remember reading that fleas and similar small insects ‘breathe’ by some form of osmosis through their skin (I know they don’t technically have skin but I’m not sure what word to use).
I’d imagine the mechanics of lungs at that scale would be problematic, not to mention the fact that air passages to and within the lungs could well be smaller than the air molecules themselves.
[hijack]I seem to remember that there was a DS9 episode that addressed the breathing problem shrunk people might face. (And afterwards, Worf tried to write a poem about the adventure.)[/hijack]
Look, any time you show people shrinking or growing in comics or movies you’re going to run the risk of getting into problems with physical reality. You know the drill – square/cube law, heat transfer, breathing, etc.
The whole thing was driven home to me when I was still a kid, reading DC’s The Atom. at one point he’d shrunk himself down ludicrously small, and one line of dialogue ran “I can breathe comfortably here in this oxygen atom!” This made me sit up and take notice – “What? He’s supposed to be breathing the atom itself! How can you breathe inside an atom?”
To their credit, DC’s writers (a lot of noted SF authors contributed to the DC comics back then) came up with some good concepts. In one comic someone shrank so small that even Green Lantern wasn’t able to see them any more, because they’d “shrunk smaller than the wavelength of light”, which I thought was cute. In another Atom comic he’s looking at individual photons, and I had to ask , if photons were “individual packets of light”, then what was he seeing them with?
Marvel comics were more fun, but DC’s comics baxck then got you thinking about science, the way Einstein did when he imagined riding on a photon.
