Re: inelastic collision (was: Re: Newton e Hooke)

In article <m28047FughsU1@mid.dfncis.de>, I wrote

the momentum transfer during the collision is actually
*two-way*, i.e., *each* body transfers some momentum to the other body.
That is, during the collision A's momentum changes (because B transfers
some momentum to A), AND B's momentum changes (because A transfers some
momentum to B).
>
[[...]]

In other words, during the collison B transfers momentum -3.75 to A,
so that A's momentum changes by Delta_p_A=-3.75.  AND, during the
collision A transfers momentum +3.75 to B, so that B's momentum changes
by Delta_p_B=+3.75.

In article <vps7vq$3laqc$1@dont-email.me>, Luigi Fortunati replied

Body B has a momentum -3 and, therefore, cannot transfer -3.75 to body
A because it does not have it.

This is mistaken.  (Linear) momentum doesn't have an inherent zero point,
so there's never a case where one body doesn't have enough momentum to
transfer some to another body.  Rather, momentum is analogous to position
on a number line, where being at position -3 doesn't prevent you from moving
a distance 3.75 either to the right or to the left.

One way to "see this in action" is to consider what the collision would
look like if analyzed in a different inertial reference frame (IRF).  For
example, let's consider an IRF which is moving to with a velocity v=-10
(i.e., moving the left at a speed of 10) with respect to Luigi's original
IRF.  In this new IRF, each velocity is the velocity in Luigi's original
IRF + 10.

In this new IRF, the speeds and momenta before the collision are
   v_A_before = +11 --> p_A_before = +55
   v_B_before =  +9 --> p_B_before = +27
   p_total_before = p_A_before+p_B_before = +82
so that after the collision, the total momentum must also be p=+82.  Hence
the common body of mass 8 must be moving at a speed of p/m = +10.25 after
the collision, and A and B's speeds and momenta after the collision must be
   v_A_after = +10.25 --> p_A_after = +51.25
   v_B_after = +10.25 --> p_B_after = +30.75
   p_total_after = p_A_after+p_B_after = +82
The velocity changes during the collision are thyus
   Delta_v_A = v_A_after - v_A_before = +10.25 - +11 = -0.75
   Delta_v_B = v_B_after - v_B_before = +10.25 -  +9 = +1.25
and the momentum changes during the collision are
   Delta_p_A = p_A_after-p_A_before = +51.25 - +55 = -3.75
   Delta_p_B = p_B_after-p_B_before = +30.75 - +27 = +3.75

Notice how the velocity changes during the collision, AND the momentum
changes and A <--> B transfers during the collision, are exactly the same
as when we analyzed the collision in Luigi's original IRF.

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