Domino effect - Its more than just a fall

There is none who hasn't heard of the domino effect. Its the chain reaction triggered by one falling object on the other (dominoes) which in turn fall on the other and so on. Simple isn't it? But when I was surfing the net reading about the energy conversions involved in a domino effect, I was amazed to see how naive I have been in thinking that the effect is nothing but a successive fall of dominoes. Here are some of the interesting aspects of a domino effect that I came across

1) The speed

The speed of the domino effect depends on the distance between the successive dominoes. The farther they are placed apart, the slower is the progression because it takes a longer time for the falling domino to knock down the next one - common sense. 

2) An Infinite arrangement of dominoes

An infinite dominoes set poses some interesting questions. Will the system continuously lose energy continuously through heat and sound and eventually come to a halt? The answer is no. The energy of the system comes from the potential energy of each of the dominoes that was stored while setting them up in a metastable position. An initial trigger to the first domino will convert its potential energy into kinetic energy while falling and a fraction of this kinetic energy will push the next domino to an unstable position thereby making it fall and converting its potential energy into kinetic. Thus the system is self sustained and never comes to a stop. In fact, as the first domino pushes the next at a speed, the second one falls faster than the first. This in turn topples the next one even faster and thus the progression is actually accelerated.

So, if the progression is accelerated, will an infinite dominoes system reach the velocity of light at one point? the answer is no again. Consider this analogy - a ball falling towards the earth's surface from about a height of 1000 km should ideally reach a velocity of 42 km/sec when it reaches the surface. But that does not happen because the atmospheric air dampens its acceleration and makes it reach a "terminal velocity" which will be constant till it touches the ground. Here energy is lost by friction and buoyancy and an equilibrium is reached. In a similar way, in a domino-effect, the energy is lost during the impact through heat and sound. this energy loss is more when the speed of impact is more. Thus the system reaches a point in time when the acceleration and energy loss reach an equilibrium and the progression will be at a constant velocity from then on.

There may be still more to a domino-effect when you consider the size and geometry of the dominoes. May be I'll look for more on this topic and write about it sometime later. From now, when you witness a domino effect, remember, there is more to it than what meets the eye! ;)

References: Wikipedia, www.physicsforums.com