Here, you are talking about a ball having some momentum p_ball bouncing
off a very massive object. The ball transfers momentum less than but
almost equal to 2p_ball to the very massive object. As viewed from the
inertial reference frame in which the very massive object (of mass m)
was initially at rest, the final momentum of the very massive object is
less than but almost equal to 2p_ball.
In the expression m^2* V^2 / (2 m) , as you consider massive objects of
greater and greater mass, the V will decrease in such a manner that mV
gets closer and closer to 2p_ball. Since we know that p=mV is bounded
above by 2p_ball, it makes more sense to take the limit of the kinetic
energy expressed as p^2/(2m). As such, in the limit m-->infinity, the
kinetic energy transferred to the very massive object goes to zero.
Note that these arguments are only true as viewed from the inertial
reference frame in which the very massive object is initially at rest.
As was pointed out to me most kindly by contributors to this list some
few weeks back, as viewed from a reference frame in which the very
massive object is initially moving in the same direction as that of the
velocity of the ball relative to the very massive object, a significant
amount of kinetic energy is transferred to the very massive object from
the ball.
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Bernard
Cleyet
Sent: Tuesday, November 14, 2006 11:43 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] momentum and energy
Classically (N) p^2/2m = (identically) m^2* V^2 / 2 m Am I crazy?
If not, then, lim: m => inf. (with v non zero*) E => . not
zero
* Which I think agrees w/ jsd == i.e. "you will find that V makes a
negligible contribution to the golf ball velocity, but a nontrivial
contribution to the conservation law."