Re: Electric gun, WORK ENERGY

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

SPECULATIONS, NOT A SOLUTION (see the problem below).

It is probably appropriate to think that the emission of e.m. waves
is a thermalizing (dissipative) process, as far as mechanical energy
is concerned. If the removal of the mechanical energy were due to
a constant force f, such as friction, then the bullet would be stopped
somewhere. (The acceleration becomes negative after the coulomb
force becomes smaller than f.) The effect of a velocity dependent
resisting force (f increases when v increases) would be similar, the
infinity would not be reached, the final velocity would become zero
at some distance from the source. Is this also true when f depends
on the magnitude of acceleration rather than on speed?
Ludwik Kowalski

A PHYSICS PROBLEM:

> The conceptual device (metallic beads on a plastic stick), used
> to discuss distributions of charges this week, is also appropriate
> to review energy at a more advanced level.
>
> There are only two beads, one firmly attached to the end of a
> stick and another free to slide without friction or air resistance.
> Suppose the m=5 grams and the Q=20 microC for each bead.
> The mass of the stick is practically infinite. The initial distance
> between the beads is 3 cm, it corresponds to potential energy
> of 120 J. A trigger is pulled and all that will turn into kinetic
> energy of the sliding bead. The final velocity will be 219 m/s.
> This is a silent killing device which does not recoil. But that
> is not my point; patents on such guns are likely to exist.
>
> According to the work kinetic energy theorem work done on
> the center of mass (by a net force) becomes kinetic energy.
> This is true for any force, even the air resistance or friction
> (negative work --> decrease in KE). In this case the net force
> = coulomb force. Note, however, that the initial acceleration
> is 800000 m/s^2.
>
> Is this significant to produce a sizable amount of e.m. energy?
> What fraction of the work done by the net force is going to be
> doing something else than increasing the kinetic energy of the
> center of mass? What would the final speed of the bullet be if
> the emission of e.m. enegy were not ignored? How small
> should the mass of the accelerated bead be for the final speed
> of 100 m/s, instead of 219 m/s? I do not have the answers.