You have an infinite row of dominoes. Each domino is the same size, weight, and distance apart from the next domino.
Ignore relativistic effects, assume that the coefficient of friction between the dominoes and the floor is excessively large, and assume the naturally occuring variables, such as sound and heat loss, do not apply.
If you were to graph the topple rate (dominoes toppled over a second) over time, what would the basic shape of the line be?
What are all the necessary variables in determining the equation of the line?
Use the variables from the previous part to create an equation that solves for the topple rate after a certain time has passed.
Given certain (ideal) conditions, I think the speed would approach infinity. Neglecting normal considerations such as air resistance and the ability of a domino to resist deformation when struck by other bricks with increasingly ludicrous speeds, the kinetic energy of a domino n would be equal to the input KE and the sum of the potential energies U of dominos 1 through n-1. In fact, the rate at which the number of dominos toppled per second would increase exponentially, as toppling event n involves more energy and is thus faster than the n-1 event.
In REALITY (or the physics-problem approximation) however, natural resistive forces (mainly air resistance) would reach an equilibrium with the conversion of potential to kinetic energy. Setting the two terms equal would yield the kinetic E at infinite t, and the system could be described fairly easily from that point.
all right, so tell me why I'm wrong!
Posted by Trystero
on 2006-09-17 05:15:14