But if we have limited resources and space, haw can you explain Olive's garden unlimited breadsticks?
In theory, yes there is no limit on how many you could put in a sequence. But due to the exponential growth, there is a physical limit (unless we have infinite resources and space)
Yes, there will be problems with the gravitational pull between the dominoes themselves, but if we consider the extreme case of a completely flat plane, where it's depth increases the further down the sequence it is (to counteract the gravitational pull of the domino), it would still be possible to make an infinite sequence.
In order to perform this experiment you have to have ground, so the first constraint is how large can a rocky planet be? You can't perform this experiment without gravity and a gas giant doesn't seem likely to work either. According to this, it's twice the radius of Earth. This gives you an 8,000 mi radius, which translates to 2 * radius * pi ~= 50,000 mi circumference.
Let's ignore the possibility of an oblate spheroid shape increasing the circumference. In fact, let's make a lot of assumptions:planet is perfectly spherical we start with a single, plain ol' domino we use domino materials to make everything each domino grows by 1.5x the previous domino's size in every dimension the next domino is set 4 times the thickness of the previous domino away
Starting with a regular sized domino and growing at a 1.5x rate, spaced 4 times their thickness apart, you can lay out 51 dominoes, the last of which is 18869 miles high, 9434 miles wide, and 2515 miles thick. The second to last domino is 12579 miles high, 6289 miles wide, 1677 miles thick, and falls 8386 miles to its target. The last domino also weighs 3.9 octillion grams, or 3.9 billion billion billion grams. Roughly 6,000 times the weight of planet Earth!!!
Umm, so we probably have to change materials halfway in to prevent the collapse of our planet. Also, I have no idea what happens after that last piece falls.
I'll put my math up on google sheets in a minute so that others can check my work and or play around with numbers if they feel so inclined.
edit 2: the second to last domino actually falls 6708 miles if you exclude its own thickness
At Olive Garden, this process is alarmingly fast.
SpaceShip Earth. When you poop that matter is eventually turned back into breadsticks.
I think the only things restricting it are the strength of your material and possibly the curvature of the Earth. At some point the domino will become unable to support its own weight or become so big that it is physically unable to lie flat on the ground (and eventually the Earth will start orbiting it, etc.). If you had an infinite flat surface and perfect building materials you could theoretically go forever.
If the mass of the Earth is M⊕ (~6 x 1024 kg), then the mass of our hypothetical domino laboratory is 2M⊕3, or ~1.7 x 1027 kg.
This is only 1700 times the mass of the Earth, so a final domino that weighs 6000 times the mass of the Earth is not doable!
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Actually no, a domino can always knock over a domino 1.5x larger than itself. You could start with a domino a millimeter tall and eventually knock over a domino as tall as the empire state building.
Won't the mass of the last domino be greater than the planet it is on? I think it would have a greater gravitational influence than the earth and therefore the planet will fall onto it, not the other way around.
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Makes sense. Thanks
This is what I was hoping for. Can I give you answer credit too?
That'd be quite the display I tell ya
RemindMe! 1000 years
There's an interesting problem for this - gravity won't effect the top of that domino nearly as much at the bottom. At 200 miles or so, the difference in gravity will fuck up our dominos.
Yes there is an upper limit that has not yet been addressed here. The velocity at the top of the dominoes increases each time. Eventually, relativity will begin to play a role as the velocity approaches a significant fraction of the speed of light. Somewhere around there, it will stop working.
Another problem is that the dominoes themselves will eventually become so large that the gravity they produce will begin to play a significant role. Eventually the dominoes will start sticking together.
Stop by /sub/shittyaskscience, they can help you with this question
so many tules. Got it
At some point doesn't the mass start to have a gravitational impact on the whole thing and probably prevent the dominoes from actually being capable of falling? In order for something to "fall" it has to be subject to some kind of gravitational pull, but if the domino itself is large enough to being the largest mass everything will just "fall" into it.
that's basically what star trek replicators are. it is coming, mark my words
At some point, you would run into failure of the materials out of which you construct your dominos. In the example gif the final domino crashes down and smashes on the ground, showing its hollow wooden construction.
Using wood with a hollow interior would probably only be reliable for 1 maybe, 2 more tiers before you would start to see structure failure to the point that triggering the next domino would not be guaranteed.
For example, when each domino impacts the next one, it's concentrating all its force along a line at the top. This causes both the moving and stationary domino to deform. Depending on the forces involved and the construction material, this could cause plastic deformation which eats up energy that would otherwise go into moving the next domino up.
At some point, your dominos could be made out of the stiffest material known and they are still going to be unable to respond in a sufficiently rigid and elastic way to propagate the chain reaction.