Conference rusure::math

    (N-1)+(N-2)+(N-3) .. .. ..

Well, let's look at the first two masses.  We'll use uppercase letters
for larger masses and lowercase for smaller.  Assume masses flow from
left to right.  Suppose we have

	A b ...

A is larger than b, so A will still be moving to the right after striking
b, but b will be moving to the right a bit faster than A.

Now, b will hit something, and we want to know whether A can possibly strike
b again.  If b hits something sufficiently large, A will certainly strike
b again.

Someone want to take it from here ?

/Eric

    Explanation to *.1
    Please note that I shall change frame of reference after impacts.
    
    
    
    
     Object  1  2  3  4  ....... N
    
    Obj 1 move right 2 to N are "stationary"  and Frame is "stationary"   
    
    Consider initial impacts only!  there will be (n-1) then N moves off to
    the right never to be seen again.
    
    
    
    NOW move the Frame of reference to object N-2.  In this Frame object
    N-1 is moving to the Left towards N-2.    the maximum number of impacts
    this time is (n-2) and object 1 shoot of to the Left.
    
    
    
    Fix the Frame of reference to object 3 and watch object 2 staert the
    whole thing again.
    
    
    (n-1)+(n-2)+(n-3) ....... (n-n) is a posible answer.
    
    Looking at the momentum and energy equations we can ignore the objects
    at the extreme edges when they "fly-off" as the next object to be lost
    from that same side must have a lower relative velocity.
    
    What I havn't considered in detail are additional impacts as the moving
    wave of object collide.  I think *.2 is the key if we consider energy
    and momentum for the lumped masses. i.e. initally object 1 and Lumped
    mass of objects 2 to N.
    
    
    I think about it over lunch. Over to you Eric.
    
    
    
    	Gregg

Imagine this configuration:

	A->  b   A

In other words, two very heavy and equal masses A sandwiching a small mass b.

The lefthand A moves to the right and strikes b.

A is large so it is still moving, but only slightly slower.  b is now moving
at about the same rate that A is.

	A->    b->    A

Now b strikes the righthand A, but since A is so heavy, it starts to move
but hardly.  b reverses direction, at almost no loss of speed.

	A->    <-b   A->

Slightly later, the lefthand A and b collide.  A is real heavy, so it continues
moving to the right, hardly slowed down.  b on the other hand, experiences
quite a bounce, since it had hit A in a head-on (both moving towards each
other), so b now moves to the right faster than before, and can overtake the
righthand A.

Can this go on forever, with endless collisions ?

I'm of course using a model here where we don't have any loss of energy due
to friction of rolling, and no energy loss during collisions.


/Eric

    reply .4
    
    What a minute. If a light b strikes a heavy A, doesn't b stop still?
    
    Under what circumstances do we have elastic colisions?
    
    The reason I am asking, I rember a toy where 4 steel balls are hung in
    a row. If you pull the left hand ball back and let it strike the other
    3 it stops dead, and the right hand ball acheives nearly the same
    velocity as the left hand ball had when it struck the middle two.
    
    This is an instance of the conservation of momentum.
    
    

    re .8
    
    Nice work with the Compose key!
    
    Note the assumption that the masses are sliding or in any case not rolling
    (else this has to be accounted for).

    My guess for the A b A situation is that b will act as a sort of agent,
    transfering momentum from the left A to the right A (and get a helluva
    banging in the process).