1. Application of energy principle to multiparticle system: For a composite system, i.e. a system which contained 2 or more particles, the energy principle is often applied to both the point system of the center of mass and to the whole system, or the “real system”. Included here is a discussion on this topic.

Application of energy principle to multiparticle system

2. Collisions involve magnetic force

Q (by chiu): In the context discussing “Collisions without contact” (see page 383), I am tempted to add the observation, that  if a collision involves a magnetic force, momentum conservation is not expected.  Is the physics correct?   If so, is this aspect discussed elsewhere in the MI text?  If not, what have I overlooked?

A. (by Sherwood): I direct your attention to problems 21.P.37 and 21.P.38 on pages
881-882. It is indeed entirely appropriate to say something about this
when discussing collisions in the mechanics course. But I wouldn't say
"momentum conservation is not expected". Rather I would say something
like this:

Next semester we will study how moving charged particles exert
"magnetic" forces on each other. These forces need not obey
reciprocity, and the total momentum of colliding charged particles
need not be conserved. However, it turns out that there is momentum
associated not only with the particles but also with the electric and
magnetic "fields" surrounding the charged particles. When this "field"
momentum is taken into account, one finds that the sum of the momenta
of the particles and the field momentum is in fact conserved. So one
may say that momentum conservation is truly a fundamental principle,
valid in the classical mechanics of Newton, the electromagnetism of
Maxwell, the relativistic mechanics of Einstein, and even in quantum
mechanics.

There is a related issue with energy, which is discussed on pages
271-272, where for some choices of system it appears that energy is
not conserved, but in fact there is energy associated not only with
the matter but also with the "field".

P.S. I attach an AJP article from many years ago which was recently
brought to my attention. The author explicitly calculates the field
momentum as well as the particle momenta in a collision between
charged particles. Click here

3. Selected topics in the Collisions chapter treated in the text.

o Categories of elastic, inestatic and perfectly inelastic corresponds to DE_int=0, DE_int>0, and K_rel=0 respectively.

o The general formula for a head-on elastic collision p1+p2=p1’+p2’ is given by vi’=2v_cm-vi, where i=1,2. It can be derived by the following.

o In the cm frame, v*i=vi – v_cm.

o In this frame the elastic collision is given by v*’i=-v*i=v_cm-vi.

o Back to the lab frame. The velocity of the final particle i is given by vi’= 2vcm –vi.

o Rutherford scattering. It is an important application of collisions in the microscopic world. Rutherford scattering involves following process. A high energy alpha particle collides with a Au-nuclei. Occasionally back scattered high energy alpha particle is observed. Such observations led to the conclusion that within an atom there is a tiny massive nucleus at the center. This laid the foundation of the present view of atoms.