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Transcription
p.242
[illegible] I suppose the bullet completes
its acceleration at some time when the
muzzle is at the end of the barrel, and that it has a
velocity v which is equal to the muzzle velocity.
It follows from this that if the gun was originally at rest,
the gun moves forward with a velocity u = mv/M
when I have supposed that all momentum is conserved.
A quantity (mv+Mv) must be constant, and if the bullet
is not fired “uncompensated” so that it has some mass left
in the tube behind it, then this equation will
hold also in a slight modified form so that u =
v(M+m)/(M+m) where m is the remaining mass of the
bullet at end of t (approximately if acceleration is small).
I presume therefore that an equal and opposite force is
exerted on the gun in such time as to give it this velocity.
The momentum of the bullet is then Mv = mv + mu,
it has velocity v. If the gun was not originally stationary, but had some initial velocity U, then the final
velocity would be V = (M+m)U + mv / (M+m). This
can easily work out a proper relation to work out.
p.243
(-1+2i) and 0.98 at 6 o'clock.
0.98 cm from the axis, which is not at all very different from the value of r.