Re: [Phys-l] momentum and energy

[John Denker <jsd@av8n.com>]

On 11/12/2006 09:16 PM, Spencer, Rob wrote:
> Greetings, I am a high school teacher and I have a question regarding an assumed elastic
> collision.  Suppose a golf ball strikes a massive wall and recoils with a velocity equal in
> magnitude to its initial velocity.  If one were to evaluate the situation with conservation of
> energy, then energy is conserved (defined to be perfectly elastic).  All of the (kinetic) energy
> remains in the golf ball.  None is transferred to the wall.  However, the wall must acquire
> momentum due to the fact the system momentum must be conserved.  So the wall has final momentum
> when it initially had none but has no kinetic energy.  I am having a hard time with an object
> having momentum but no energy conceptually...any guidance would be appreciated.

That's a classic!!!

My father foisted that question on me when I was about 8 years old,
and it took me many, many years to figure it out.

The trick is here:
> recoils with a velocity equal in magnitude to its initial velocity.

That's strictly true in the CM frame and approximately /but not exactly/
true in the lab frame.

The earth /must/ recoil a little bit.

As another way of saying the same thing, infinities are tricky.  Taking
the limit of an infinitely-massive earth is asking for trouble, especially
if the limit is taken too early in the process.

The fix is simple:  Use M and V to denote the mass and velocity of the earth,
then treat everything just like any other two-body collision problem.  You
will find that M is large and V is small, such that MV is not trivial.
you will find that V makes a negligible contribution to the golf ball
velocity, but a nontrivial contribution to the conservation law.