How does a row of dominoes behave?

Question

If there was an infinite row of perfectly align dominoes on a floor with a high coefficient of friction (so the dominoes act as if they are on a hinge), does the rate of dominoes toppled per second only reach a maximum rate at the point of infinity or does is there a definite maximum value or will the value keep increasing forever (forgetting about reletivistic issues)? (assume that the dominoes lose energy when they hit eachother)

The friction between the FLOOR and the dominoes is high but there is no friction between the dominoes. So rather than the dominoes slipping and making things undeterminable, the dominoes topple as if they were on hinges.

In response to DavidF:
One thing to take into account though is that the collision between each domino is not elastic, so the momentum is not completely transfered between each domino. As a little demonstration, just take two books and place them like two dominoes and hold them with you hand at the bottom. As you tilt the first one over and it touches the second which is also forced to tilt, notice that the first is supported by the second. And because the first will never stop (since it is an infinite row) the whole chain is one body that keeps on adding and losing momentum.

Answer 1

the dominoes will reach a terminal velocity.. based upon their weight and the friction of the air as they fall... just like dropping one from an airplane.. and having it always large face downward (not edgewise)

Answer 2

If there is infinite friction between dominoes and ground, but 0 friction between dominoes and each other, I think it would keep accelerating ad infinitum (ignoring relativity as you said). The reason is this: As a single domino topples, its center of mass is lowered by about half of the height of the domino. This causes the Gravitational Potential Energy (GPE) to be transferred into Kinetic Energy (KE). Because the domino is now in motion, it has non-zero momentum. When it collides with the next domino in line, domino #1 comes to a halt (during the collision, once it has fallen) and must therefore transfer its momentum to domino #2. The whole process starts over, except that domino #2 starts out with a certain momentum which is then added to the KE it will get from its GPE. It then has a slightly higher velocity than domino #1 (because momentum=mass*velocity). This continues down the row in a sort of "domino effect" with each successive domino adding just a little bit more momentum to the total. This would obviously never happen in real life because we're assuming infinite hinged frictionless dominoes, and that contains 2 impossibilities and one thing that would be cheating.

Edit: Momentum is conserved in any closed system free from outside influence. The extra amount that a domino falls after the effect has gone more than a few dominoes away is so close to 0 that it's not even worth trying to calculate. If we assume that the dominoes are an open system (meaning that all calculations are done from the reference point of the surface they're "hinged" to, that way we don't have to consider the dominoes as "pushing back" on the floor because the floor is defined as being stable), then all the momentum (except for the infinitesimal amount I mentioned earlier) will be in the 5 or so dominoes that fell most recently. As you agree, each falling domino adds some momentum to the total of the system. (As I write this, I get more and more confused.) The momentum to "cancel out" this momentum is in the Earth/floor which we defined as static. Since we have a steadily increasing momentum in a more or less steady amount of mass, we must therefore get a steadily increasing velocity. Don't take my word for this just yet because I need to think about it some more. This is an interesting problem, and I'll spend some more time working on it.

Edit again: I'm pretty much stuck. I haven't yet learned anything about torque and that stuff, so I've been relying on geometry, 11th grade physics, and common sense. Right now my guess is that the falling rate will asymptotically approach a finite value, but that's just a guess.

Answer 3

as long as the dominoes are tall enought that the energy gained from striking the next domino is more than that lost by the elasticity in the collision (which would be the case except for very short, very elastic dominos), then each domino in the chain would add slightly to the momentum of the chain as it strikes the next one, so it would reach a maximum rate at infinity.

assuming, of course, that the dominos don't break due to the force of the impact, and ignoring effects due to air resistance.

Answer 4

If there was a high coefficient of friction, at the point of inifinity (and much before that) the number of dominoes toppled per second would be zero. Only if there was no friction would a row of infinite dominoes be able to keep toppling.

Answer 5

If this took place on earth than it would incread to the speed of the rotarion of the earth than slowly decrease in speed due to the loss of energy when the dominoes collide but they will never come to a complete stop.

Answer 6

True or false?

You'd be a happier person if you'd let a few slices of Domino's pizza topple down yer throat right about now.

Answer 7

think of the dominoes as awave of water, aslong as there is more water in front of it ,it can move indefinitly also the distance between the dominoes just like the depth of the water determines the amount of energy it transfers

Answer 8

If there's air resistance then there would be a maxium speed. If no air resistance, then you would still have momentum of each domino to contend with.

Answer 9

Search the web - "domino principle"

Answer 10

Like an animal, in a predicable motion, according to gravity.