How can you calculate the speed at which dominoes fall?

[JVS]

Consider this problem. You have a 100 foot line of dominoes. You want to calculate how long it will take for the dominoes to all fall over if you knock over the domino at one of the ends. Does the path of fallen dominoes expand at a constant rate or does it accelerate? If it accelerates in what manner? What factors might effect these rates? What are the effects of curves?

[kick-ass-bob]

1. gravity works at a constant rate

so I would think that if they are evenly spaced, no matter of turns, they fall at the same speed as the one before.

That does assume that you have them the same distance apart, so they hit the next at the same point.

[JVS]

2. Sounds reasonable, but although we describe the dominoes as falling.

We really aren't measuring a fall so much as we're observing the rate of a sequence of actions (the falls)

[NNadir]

23. Here are some parameters you would include depending on your desired

level of accuracy.

1) The distance between the dominoes.

2) The levelness of the floor.

3) The nature of the material beneath the dominoes.

4) The density of the air (i.e temperature and pressure)

5) The composition of the dominoes.

There are certainly other factors.

[Goldmund]

4. But there is one difference

When the first domino falls, no other domino is pressing on it. When the second falls, the first hits it at some speed, so there is an initial velocity associated with the fall. Then that domino hits the third one with this initial velocity incorporated into its own velocity, so the initial velocity of the third domino is even greater. That effect probably stops growing after a few dominos -- but the first several dominos definitely fall at an increasing rate.

[seriousstan]

6. No they do not

they increase in speed because you are actually stacking the weight of the dominoes falling. You can actually have exponentially larger dominoes in the line.



http://www.exo.net/~pauld/activities/mathematics/dominofall.html

[kick-ass-bob]

9. Ha! That's why I became an economist instead of a physicist!

:D

We just hold shit constant if we want to!

[seriousstan]

3. This is very complicated, but smarter folks than myself have tried....here

http://64.233.167.104/search?q=cache:uHGRQnvacvoJ:www.lorentz.leidenuniv.nl/~jmjvanl/domino.pdf+domino+falling+speed&hl=en&lr=lang_en

[Speck Tater]

20. A better link

that retains all the illustrations and equations: http://www.lorentz.leidenuniv.nl/~jmjvanl/domino.pdf

[seriousstan]

27. Thank you for a beautiful link.

It illustrates the math much better than mine.

[tridim]

5. It's way too random

In a vacuum, with perfectly shaped dominoes, perfectly spaced, in a perfectly strait line and constant friction I'd guess there would still be a fairly large error due to chaos. Not to mention, falling dominoes don't fall all the way, they rest on the next domino. It would certainly be an interesting math problem, even with the error.

I would just set up 10 and calculate how long it takes them to fall and then extrapolate.

Edit: I have a physics module in my 3D program.. Maybe I'll try it in a "perfect world". My guess is they won't fall consistently even when simulated due to computational rounding.

[sniffa]

7. i'd have to munch on that

but off the top of my head, i'd say the speed accumaLates since:

f = (m)(a) where a is constant, m is increasing with each dominoe's mass. so the force is increasing (it wouLd aLso depend on the amount of space between dominoes - since more of a domino Leaning on the next domino = more weight, etc).

so, i think if you have your distance, and domino mass the speed can be found.

damn you! now i'm gonna have to dig up text books when i get home.

[Goldmund]

10. But if the force is increasing, that doesn't mean that the acceleration...

...is increasing -- since the inertial mass of the system is increasing as well. It's the old Galileo/leaning tower of Pizza lesson -- all objects fall at a constant rate regardless of mass.

That doesn't mean that they fall at the same velocity, because their initial velocity may not be the same -- and it isn't in this case, because the first domino has no initial velocity (other than what the push with your finger gives it), but the subsequent domino gets bumped by the first one before it starts falling.

[dvaravati]

8. speed formula

Speed= distance divided by time.
Then find the average by number of dominoes.

[Goldmund]

11. So why don't you do it?

You have 100 dominos. 2 inches tall.

[JVS]

12. kick

[patcox2]

13. Calculate the inertial resistance to being struck by another.

You have to know the inertial resistance, (my probably incorrect term) i.e., the speed of acceleration of the standing domino upon being struck by another domino. It will involve the resonant ferquency, probably, the dimensions of the domino, its weight, the degree to which its CG actually raises up as it falls (as a square object tips onto one corner, its center of gravity rises higher, this is a major component of the resistance to tipping. This will tell you how long it takes for the domino to fall over.

Back in my engineering school days, this would have been a challenging but probably doable problem.

The other way would be to set some up and time them.

[JVS]

14. kick for people who are gainfully employed and thus presumably smart

[HEyHEY]

16. presumably?

Well, in that case I suggest taking the rate of gravity divided by the weight of a domino...PLUS considering that domino will speed up at a ratio determined by the two previous pieces of information. I've determined it will begin falling at o and by the time it has fallen will have reached speeds of 230 km/hour. Give or take.

[JVS]

17. That's some mighty fine J-School math

[HEyHEY]

18. Math? there was no equation involved I just went with my gut

Actually the gut of the nerd I beat it outta!

[JVS]

19. Well your gut was wrong

[HEyHEY]

21. Dang, that nerd's gonna get another beating

[JVS]

22. Bring it on! Math department rolls deep, we'll fuck your shit up

or we'll sic our legions of undergrads on you

[HEyHEY]

24. ooo look out, it's the braceface brigade!

:scared:

[JVS]

25. None of us have braces

We even have 2 canadians

[HEyHEY]

26. Canadians eh?

Musta sent em down to infiltrate your universities and steal stationary.

[HeyManThatsCool]

15. Noooo clue

but good ?