Knocking down the Eiffel Tower

Classical Mechanics Level 1

As shown in the video above, a small domino can knock over a bigger domino that is taller, and heavier than itself. Subsequent dominos can do the same, so that eventually, the chain can knock down a domino of any height (even one as tall as the Eiffel Tower). How is this possible?

Each domino saves a little momentum so it can always help knock the last one down. Input energy has to tilt the first domino enough to fall. Gravity does the rest of the work. Conservation of momentum, the first domino has to be pushed very hard. Conservation of energy, it actually takes the same amount of work to topple any size domino.

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Josh Silverman by Josh Silverman

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5 solutions

Discussions for this problem are now closed

The energy to topple a domino needs only to move the center of mass of the domino to go outside its base. This energy is very small since domino is thin with a narrow base and a high center of mass that reduces the applied force needed to topple it. So a small domino can topple a bigger one before it.

14 Helpful 0 Interesting 0 Brilliant 0 Confused
Yash Karavat
Jul 30, 2014

As soon as the first domino falls. it passes some of its momentum to the next domino which imbalances it and it starts to fall in the forward direction. It repeats the job done by first domino and this chain can go on upto any limit. Gravity is the factor which is stopping the domino from coming to its equilibrium position and thus the is no stopping force on domino to bring it to its neutral position.

6 Helpful 0 Interesting 0 Brilliant 0 Confused

well ,i don't agree with the solution. what if angular momentum transfer is not enough?just ensuring toppling of first block is not enough.

A Former Brilliant Member - 6 years, 10 months ago

Yes, but it is given that the blocks do actually fall.

Daniel Liu - 6 years, 10 months ago

I Agree with Daniel! Since the problem clearly shows the blocks do fall! There is no point in the above argument which would only hold if that info. wasent given...

Shreyas Kumar - 6 years, 10 months ago

Input energy has to tilt the first domino enough to fall. Gravity does the rest of the work

Prajwal S Acharya - 6 years, 10 months ago

How is the energy of the domino gets built up from a very small energy that we impart to the first one?

Vibin Shalom - 6 years, 10 months ago

Cuz there is continuous force acting on every domino right even before the smaller ones started to topple! That's acceleration due to gravity! But it was getting canceled due to it's position! once there was a little tilt..(i.e a minor shift in equilibrum!) - BAM!! goes the tower!

Shreyas Kumar - 6 years, 10 months ago
Liam Clink
Sep 20, 2014

Any angular displacement on a domino such that the center of gravity passes over the ground contact surface will cause it to fall under the force of gravity. Therefore any impulse that is sufficient to create this angular displacement will work. The only discrepancy that I see here is that the Eiffel tower is attached to the ground and has a foundation, it wouldn't just topple like a domino.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Fortunately, we weren't trying to topple the Eiffel Tower (despite the name of the problem), just a domino AS TALL AS the Eiffel Tower.

Sean Henderson - 6 years, 7 months ago
Paul Josephson
Aug 9, 2014

It's because the potential energy of the smaller domino is greater than the force of inertia of the next larger domino. Tipping the smaller domino converts its potential energy into kinetic energy (i.e. gravity 'doing the work' of pulling the domino down. To tip over its slightly larger neighbor, the smaller domino need not have enough energy to lift its larger neighbor, it only need overcome its neighbor's inertia. Once it overcomes this inertia, gravity pulls down the larger neighbor, converting its potential energy to kinetic.

Little guys all over the world know this phenomenon as

"The Bigger they are, the harder they fall".

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Emmanuel Lopez
Aug 8, 2014

Think of all the dominoes as a system that is unstable. Key word here is "unstable". Now it could have been a wrecking ball or anything, but it just so happens that each domino has enough kinetic energy to give the next domino enough energy to start it's "reaction" that converts potential to kinetic energy.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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