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Re: [Phys-l] conservation versus constancy



On Oct 17, 2006, at 2:54 PM, Bob LaMontagne wrote:

I don't follow the claim about the work being zero in one frame implies it
is zero in all others.

Indeed, it doesn't. It's easy to show that if the "center of mass work" (or "pseudowork" or whatever you want to call it, i.e., the integral of F_net dot dr_cm) done on an object in one inertial frame is W, then the work done in another inertial frame moving at velocity u relative to the first is

W' = W - u dot delta_p

where delta_p is the change in momentum of the system. The change in momentum is determined by the impulse which is frame invariant in Newtonian mechanics. The change in kinetic energy, however, is not frame invariant in general nor, therefore, is the center of mass work.

In the particular case cited, the impulse is zero and in that very special case the work is frame invariant.

John Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://outlawsofphysics.com>