Re: [Phys-l] conservation versus constancy

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Imagine the moon and a baseball so far away from any other objects that
they are both moving along one and the same straight line path, with the
moon initially ahead by a center-to-center distance d as viewed from an
inertial reference frame from which we view things throughout the
proceedings.  Call the initial position of the baseball in our frame
point A.  Further imagine that the moon is not rotating and that there
is a hole drilled all the way through it.  The ball passes through the
hole and the next time we check on things, the baseball is a
center-to-center distance d ahead of the moon at a point we call point B
in our reference frame.  The baseball will have the same kinetic energy
at point B that it had at the start of observations.  So what kind of a
sling shot effect is that?  The answer is that the baseball gets to
point B a lot sooner than it would have had there been no moon between
point A and B.  It speeds up all the way to the center of the moon and,
after it passes the center of the moon, even though it is then slowing
down all the way to point B it is still going faster then it was at
point A, in fact, it is never going as slow as it was at the start of
observations until it gets to point B.

If the force were repulsive we would have an anti-slingshot effect.
Assuming the ball could get past the repulsive moon, it would again have
the same kinetic energy at point B but this time it would always be
going slower on its trip from A to B than it would if there were no
repulsive moon in between A and B.

How do we know that the kinetic energy of the baseball at B is the same
as it was at A?  Now look at the process in the center of mass frame
where the center of mass of the system is essentially at the center of
mass of the moon.  The work done on the baseball as it moves from the
center of the moon, to a distance d away from the center of the moon, is
the negative of the work done as it moves from a distance d away from
the center of the moon to the center of the moon.  Hence the net work
done on the baseball is zero.  By Galilean relativity, if the work done
on the baseball is zero in one frame, it is zero in all frames.  There
is zero net work done on the baseball, so no there is no net change in
the kinetic energy of the baseball.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Bob
LaMontagne
Sent: Tuesday, October 17, 2006 12:06 PM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] conservation versus constancy

> > Let me propose a slightly different example
> > than gravity to get your thinking going on
> > the slingshot effect. ...