Re: Questions you love/hate to have asked

[palmer@sfu.ca (Leigh Palmer)]

> How can one explain, phenomenologically (wow) what determines the amount
> of momentum transferred to another object. Or must we rest on "the
> equation says so and the equation is a model of reality."

I don't think that you can. The question assumes that momentum is a
quantity, like caloric, which inheres to a body and which can be
transferred to another body. Momentum's not like that!

Two ways to demonstrate that bodies don't "have" momentum:

The momentum of a body depends on the frame of reference in which one
calculates it. It is a physical quantity, but it is like "the distance
of the center of mass from Mount Everest". It is a quantity which can
be calculated and always remains the same in the frame in which Mount
Everest and the system are both at rest, so long as no net external
force acts on the system. Surely this quantity does not inhere to any
body. Momentum is like that.

The other way is to note that in an elestic collision a small body is
capable of transferring twice its momentum to a much larger body
initially at rest, and much, much more to a large body moving toward
it. When this consequence of the law of conservation of momentum is
pointed out to the student (who I judge is a very bright one to have
asked the question) he will soon figure out what is meant by an
abstract function of the state of a system. To drive the point home
you should do the stacked ball demo that has been discussed here.

How can one possibly do better than to emphasize that the equation
says so, and it is a true expression of reality which is derived
ultimately from a simple symmetry property of Nature? That is the
essence of the perception of beauty we wish to have our students
share with us. My attitude is that it's really neat that there is a
quantity* that can be calculated by a seemingly arbitrarily
constructed formula representing nothing like a counting number,
which nevertheless behaves like a counting number. Don't you agree?

Leigh

*Many such quantities exist, of course. Linear momentum of a system
of particles is only three of them.