- #1
Gloyn
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Homework Statement
Hi!
I have found an interesting statement. It says, that if we have a system of two masses and a wall (all collisions will be elastic ones) with one mass (lets label it as 1) trapped between the other mass (2) and the wall and if there is no friction, then if ratio of masses m2/m1=1, then number of collisions between the masses will be 3, when m2/m1=100 then there will be 31 bounces, if m2/m1=100.000.000 then there will be 31415 collisions etc, the number of collisions will approximate more and more numbers in Pi. How do I explain it?
Homework Equations
Conservation of momentum, Newton's Law of Restitution
The Attempt at a Solution
I have calculated several velocities of masses to see if there is some simple rule. What I got is that the velocity of 2nd mass is:
[tex]V_1=v\cdot \frac{\alpha-1}{\alpha+1}[/tex]
[tex]V_2=v\cdot \frac{\alpha^2+4\alpha-1}{(\alpha+1)^2}[/tex]
[tex]V_3=v\cdot \frac{\alpha ^3 + 13\alpha^2+15\alpha-5}{(\alpha+1)^3}[/tex]
So denominator seems to be fairly regular, but numerator is rather wild.