Re: [Phys-l] conservation versus constancy

["Bob LaMontagne" <rlamont@postoffice.providence.edu>]

I don't follow the claim about the work being zero in one frame implies it
is zero in all others. In a collision between identical steel balls (one
moving and the other at rest in the lab frame), no work is done in the CM
system because there is no displacement of the contact point during the
collision. In the lab frame, there is a displacement of the contact point,
resulting in positive work being done on one ball with the same amount of
negative work being done on the other. One ball slows down and stops, the
other goes from rest to the original speed of the other. The NET work may be
zero but the individual works are done on different bodies, so the effects
are different. This is a primitive slingshot effect. A better one is to have
the incoming ball to be many times more massive. The lighter one picks up
twice the speed of the original due to the work done on it in the lab frame.

A positively charged, fast moving, heavy sphere hitting a positively charged
light one at rest produces exactly the same effect - even without direct
surface contact. That is easy to see. So why should the attractive case be
so different?

Bob at PC

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Jeffrey Schnick
> Sent: Tuesday, October 17, 2006 1:58 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] conservation versus constancy
>
> 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. ...
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