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I recently came across a new double domino effect that uses brick.
So, I'm on a construction site where they've very kindly lent me 48 bricks.
We're going to knock them over, and see if it works.
Okay, here we go.
[bricks clunking]
[bricks clunk faster]
Aaahhh!
Come on, that one brick.
[bricks clunk fast again]
There we go.
That toootally counts.
[final brick clunks]
Okay, I'm going to count that as effectively working well, to a bit stopped.
But as you can see, I'm on a very uneven ground,
and it's actually sloping uphill a bit,
so I'm pretty happy with only one, one and a half stoppages on the way back up.
So, the wave on the way down of the effectively, dominoes falling over,
is all very straight-forward.
That's ya standard domino effect.
The second wave that comes back up again,
there's a lot more interesting, and we can look at the mathematics of why that happens.
So I started with the bricks lying pretty much in position, and then lifted them all up,
onto one end, but it fall over like dominoes.
But, when they fall over, if they can't fall all the way flat,
the next one ends up resting just on the edge of that one,
this one ends up one the edge of that one, this one ends up one the edge of that one.
It is only when the wave gets right to the end,
and the last brick can lie flat, that the brick behind it can now also lie flat,
and the wave goes back in the other direction.
Let's take a closer look at the geometry of this situation.
The bricks are 21 centimeters long,
and I have positioned them exactly 21 centimeters apart.
They are six centimeters wide.
Now, if the bricks were lying flat,
there would be plenty of room for them all to hit the ground.
But they're not!
Each one sticks back slightly.
If we want to calculate how much it's overhanging the brick behind its position,
we... could look at the angle theta because if we complete this, we have a right angled triangle.
Assuming that the bricks lay flush up here,
now the cos of that angle is 6 divided by 21.
We can work that out, but, we actually don't have to.
We only care about this distance here, d.
We don't need to work out theta because we've now got another right angle triangle,
with Theta in it, which means we can just use the fact that they're similar triangles,
that d is six squared divided by 21, which is 1.7 centimeters.
Now there is an argument that instead of calculating that d distance,
I should actually be looking at the contact length,
which we could do, but I just like the fact that for any bricks you use,
if you want to calculate d,
It's always their width squared, divided by their length.
So that is the double domino effect, with bricks, explained.
Thank you for watching this video on my stand-up maths channel.
The usual, subscribe, etc.
For people who support me on Patreon, as well as the bonus footage of how I set this all up,
I'm also going to upload the full 4k video,
from the GoPro, of the effect falling over.
So, you'll find all of that on Patreon.
For everyone else, thank you so much for watching.
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