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Electric gun, WORK ENERGY



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 218 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. were not ignored? How small should the
mass of the accelerated bead be for the final speed of 100 m/s,
instead of 218 m/s? I remember seeing problems like this
somewhere, very long time ago. I do not have the answers.
Ludwik Kowalski
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To understand is to find a satisfactory causal relation.
To explain is to express that understanding.
To teach is to promote understanding.
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